"The road to the convention goes through New York for both the Democrats and Republicans," said Lee Miringoff, director of the Marist College Institute for Public Opinion, which conducted this survey. "Right now, the front-runners look like they will erase recent setbacks and add significantly to their delegate margins."
In the Republican race, Trump gets support from 54 percent of likely Republican primary voters - followed by John Kasich at 21 percent and Ted Cruz at 18 percent.
10 facts about Hillary Clinton you may not have known:
Hillary Clinton 10 Facts
NBC Poll: Trump, Clinton hold sizable leads in New York
1. She went by her maiden for years after she married Bill in 1975. She went by "Mrs. Bill Clinton" shortly after her husband lost the 1980 Arkansas gubernatorial election in part because voters had questioned their marriage's stability.
(Photo by Douglas Burrows/Liaison)
2. She once described herself as a tomboy who wanted to be an astronaut, and wrote to NASA as a 12-year-old about how she could become an astronaut. They sent her a reply, clarifying that NASA didn't accept women in their astronaut program.
(Photo by Karin Cooper, Getty)
3. She coined the term "vast right-wing conspiracy" to explain the intense scrutiny her husband faced when news of his affair with Monica Lewinsky first emerged, though she later said in a statement that she had been misled by her husband about the affair.
(Photo by Susan Walsh, AP)
3. She was the student speaker picked to give the commencement speech at Wellesley, and received a standing ovation.
(Photo by John Mottern, AFP/Getty Images)
5. Her parents were Republicans, and she herself served as the president of the Young Republicans club at Wellesley.
(Photo by Ron Frehm, AP File Photo)
6. In 1974, she was one of only three women out of 43 lawyers who worked on the inquiry into whether President Nixon would be impeached.
(Photo by David Hume Kennerly/Getty Images)
7. She named her daughter Chelsea after Joni Mitchell's song "Chelsea Morning."
(Photo by Daniel Berehulak/Getty Images)
9. She was the first first lady to hold a postgraduate degree (though every first lady since has held one), and up until her husband was elected president, her salary had been higher than his.
(Photo by Chris Ocken, AP)
9. She says she met Bill Clinton at the Yale law library when she approached him and said, "Look if you're going to keep staring at me, and I'm going to keep staring back, I think we should at least know each other. I'm Hillary Rodham. What's your name?"
(Photo by Mark Philips, AFP/Getty Images)
10. Her mother told her that she had been named after Sir Edmund Hillary, who was the first man to to climb Everest, despite the fact that he had done so five years after she was born. A spokesperson for Clinton has said that this was a "sweet family story her mother shared to inspire greatness in her daughter, to great results I might add."
(Photo by Vincent Laforet, AFP/Getty Images)
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If Trump wins with more than 50 percent of the vote both statewide and in each of New York's 27 congressional districts, he'll walk away with all of the state's 95 delegates - more than making up for what he lost last week in Colorado and Wisconsin.
Sixty-four percent of likely New York Republican voters say the Republican Party should still nominate Trump for president if he's won the most delegates but not enough to be nominated on the first ballot, versus 28 percent who believe the party should nominate someone else under those circumstances.
Clinton up 14 points over Sanders in the Empire State
In the Democratic race, Clinton is ahead of Bernie Sanders among likely Democratic primary voters by 14 points, 55 percent to 41 percent.
Clinton leads Sanders among African Americans (68 percent to 28 percent), those ages 45 and older (66 percent to 30 percent) and women (58 percent to 38 percent).
Sanders, meanwhile, holds the advantage among those younger than 45 (62 percent to 37 percent) and those who describe themselves as "very liberal" (59 percent to 40 percent). The two are running roughly even among men and Latinos.
Geographically, Clinton is ahead of Sanders in New York City (58 percent to 39 percent) and in the suburbs (61 percent to 36 percent), but Sanders holds a one-point lead in Upstate New York (49 percent to 48 percent).
Strikingly, 30 percent of likely Democratic voters who support Sanders say they wouldn't support Clinton in a general election, compared with 15 percent of Clinton voters who say that about Sanders.
Yet both Clinton and Sanders easily beat Trump, Cruz and Kasich in hypothetical general-election matchups in the blue state of New York.
The NBC/WSJ/Marist poll was conducted April 6-10 of 557 likely Democratic primary voters (margin of error plus-minus 4.2 percentage points), 259 likely Republican primary voters (plus-minus 6.1 percentage points) and 1,987 registered voters (plus-minus 2.2 percentage points).
Donald Trump through the years:
Donald Trump through the years
NBC Poll: Trump, Clinton hold sizable leads in New York
Real estate developer Donald Trump annouces intentions to build a $100 million dollar Regency Hotel. (Photo by John Pedin/NY Daily News via Getty Images)
UNITED STATES - MARCH 02: Donald Trump with Alfred Eisenpreis, New York City Economic Development Administrator. Sketch of new 1,400 room Renovation project of Commodore Hotel. (Photo by NY Daily News Archive via Getty Images)
NEW YORK, NY - 1980: Donald Trump and Ivana Trump attend Roy Cohn's birthday party in February 1980 in New York City. (Photo by Sonia Moskowitz/Getty Images)
UNITED STATES - MAY 26: Donald Trump stands behind architect's model of City Hall Plaza. (Photo by Frank Russo/NY Daily News Archive via Getty Images)
Donna Mills and Donald Trump during 1983 Annual American Image Awards at Sheraton Center in New York City, New York, United States. (Photo by Ron Galella, Ltd./WireImage)
Portrait of real estate mogul Donald John Trump (b.1946), smiling slightly and facing to his right, 1983. New York. (Photo by Bachrach/Getty Images)
New York real estate magnates Steve Ross, right, and Donald Trump, left, announce agreement, Thursday, August 1, 1985 in New York, to merge the Houston Gamblers and the New Jersey Generals United States Football League teams. Ross heads a group of investors that last week agreed to buy the troubled Houston franchise. (AP Photo/Marty Lederhandler)
Real estate magnate Donald Trump poses in front of one of three Sikorsky helicopters at New York Port Authority's West 30 Street Heliport on March 22, 1988. (AP Photo/Wilbur Funches)
Ivana Trump and Donald Trump during Mike Tyson vs Michael Spinks Fight at Trump Plaza - June 27, 1988 at Trump Plaza in Atlantic City, New Jersey, United States. (Photo by Ron Galella/WireImage)
Donald Trump and his wife, Ivana, pose outside the Federal Courthouse after she was sworn in as a United States citizen, May 1988. (AP Photo)
NEW YORK, NY - DECEMBER 4: Billionaire Donald Trump and his wife Ivana arrive 04 December 1989 at a social engagement in New York. (Photo credit should read SWERZEY/AFP/Getty Images)
Shown in photo is Donald Trump, Nov. 20, 1990. (AP Photo/Mark Lennihan)
Billionaire developer Donald Trump, right, waits with his brother Robert for the start of a Casino Control Commission meeting in Atlantic City, N.J., March 29, 1990. Trump was seeking final approval for the Taj Mahal Casino Resort, one of the world's largest casino complexes. (AP Photo)
Developer Donald Trump, center, is flanked by super middleweight champion Thomas Hearns, left, of Detroit, and Michael Olajide of Canada at a news conference in New York Thursday, Feb. 15, 1990. The three announced the super middleweight title bout at Trump Taj Mahal Casino Resort at Atlantic city, N. J on April 28.(AP Photo/Timothy Clary)
Real estate magnate Donald Trump and his girlfriend Marla Maples are seen at the Holyfield-Foreman fight at Trump Plaza in Atlantic City, N.J., April 19, 1991. (AP Photo)
Donald Trump and Daughter Ivanka Trump during Maybelline Presents 1991 Look of the Year at Plaza Hotel in New York City, New York, United States. (Photo by Ron Galella/WireImage)
NEW YORK, NY - APRIL 7: Donald Trump touches 07 April 1993 Marla Maples stomach to confirm published reports that the actress is pregnant with his child. The two arrived for Maples appearance in the Broadway musical 'The Will Rogers Follies'. (Photo credit should read HAI DO/AFP/Getty Images)
NEW YORK, NY - DECEMBER 21: US business tycoon Donald Trump(C) enters the PLaza Hotel in New York past supporters 21 December 1994. Hundreds of supporters showed up at a news conference where Trump denied a New York newspaper report that the Sultan of Brunei had bid 300 million USD to buy the Manhattan hotel. (Photo credit should read DON EMMERT/AFP/Getty Images)
FILE--This is a 1994 file photo of Donald Trump. Trump said Wednesday, Oct. 23, 1996 he has bought the Miss Universe, Miss USA and Miss Teen beauty pageants from ITT. ``It's a done deal,'' Trump said in a telephone interview. ``It's a very, very great entertainment format. It gets very high ratings, it's doing very well and we'll make it even better.'' Trump declined to say how much he paid. Asked if a New York Post source was correct in saying the deal was worth tens of millions of dollars, Trump replied, ``Why not? (AP Photo/Jim Cooper)
FLUSHING MEADOWS, UNITED STATES: Donald Trump and his girlfriend Celina Midelfar watch Conchita Martinez and Amanda Coetzer 07 September at US Open in Flushing Meadows, NY. AFP PHOTO Timothy CLARY (Photo credit should read TIMOTHY CLARY/AFP/Getty Images)
Donald Trump and Christine Whitman during Opening of New Warner Bros. Store in Trump Plaza Casino at Trump Plaza Casino in Atlantic City, New Jersey, United States. (Photo by Ron Galella/WireImage)
In this June 7, 1995 file photograph, Donald Trump is seen above the floor of the New York Stock Exchange after taking his flagship Trump Plaza Casino public in New York City. Trump Entertainment Resorts Inc., based in Atlantic City, New Jersey, filed for Chapter 11 protection on Tuesday, Feb. 17, 2009, in the U.S. Bankruptcy Court in New Jersey. Trump and his daughter Ivanka resigned from the company's board Friday, Feb. 13, 2009, after growing frustrated with bondholders. (AP Photo/Kathy Willens,File)
Celine Dion, husband Rene, Donald Trump & Ivanka Trump (Photo by KMazur/WireImage)
Entrepreneur Donald Trump watches an undercard fight as an unidentified companion whispers into his ear before the start of the Mike Tyson versus Francois Botha bout at the MGM Grand Hotel & Casino in Las Vegas, Nevada, Saturday, Jan. 16, 1999. (AP Photo/Eric Draper)
Developer Donald Trump holds an umbrella as he walks Saturday, Nov. 9, 2002, to the 11th green of the Ocean Trail Golf Club in Rancho Palos Verdes, Calif. Trump plans to turn the beleagured golf club into a world class course. Trump intends to close on the golf club by December and hopes to begin improvements by January. He could reopen the course, 20 miles south of Los Angeles, as early as June. (AP Photo/Damian Dovarganes)
Entrepreneur Donald Trump (L) and Rev. Al Sharpton speak at a ribbon cutting ceremony for Sharpton's National Action Network Convention April 5, 2002 in New York City. The group aims to further the development of civil rights. (Photo by Mario Tama/Getty Images)
Donald Trump and his girlfriend Melania Knauss attend the Marc Bouwer/Peta Fall/Winter 2002 Collection show February 14, 2002 during Mercedes-Benz Fashion Week in New York City. (Photo by George De Sota/Getty Images)
NEW YORK, UNITED STATES - DECEMBER 06: WBC Kampf im Schwergewicht 2003, New York/Madison Square Garden; Vitali KLITSCHKO/UKR - Kirk JOHNSON/CAN; Donald TRUMP als Zuschauer (Photo by Alexander Hassenstein/Bongarts/Getty Images)
FOXBORO, MA - JANUARY 10: Donald Trump stands on the sidelines before the start of the AFC divisional playoffs between the New England Patriots and Tennessee Titans on January 10, 2004 at Gillette Stadium in Foxboro, Massachusetts. Temperatures have reached as low as 7 degrees in the Foxboro area. (Photo by Al Bello/Getty Images)
US tycoon Donald Trump arrives to speak at the annual Conservative Political Action Conference (CPAC) at National Harbor, Maryland, outside Washington, on February 27, 2015. AFP PHOTO/NICHOLAS KAMM (Photo credit should read NICHOLAS KAMM/AFP/Getty Images)
NASHVILLE, TN - APRIL 10: Donald Trump speaks during the NRA-ILA Leadership Forum at the 2015 NRA Annual Meeting & Exhibits on April 10, 2015 in Nashville, Tennessee. The annual NRA meeting and exhibit runs through Sunday. (Photo by Justin Sullivan/Getty Images)
WASHINGTON, DC - MARCH 24: Real estate mogul and billionaire Donald Trump attends Golf legend Jack Nicklaus' Congressional Gold Medal ceremony in the U.S. Capitol Rotunda March 24, 2015 in Washington, DC. Trump announed on March 18 that he has launched a presidential exploratory committee. (Photo by Chip Somodevilla/Getty Images)
DES MOINES, IA - MAY 16: Businessman Donald Trump speaks to guests gathered for the Republican Party of Iowa's Lincoln Dinner at the Iowa Events Center on May 16, 2015 in Des Moines, Iowa. The event sponsored by the Republican Party of Iowa gave several Republican presidential hopefuls an opportunity to strengthen their support among Iowa Republicans ahead of the 2016 Iowa caucus. (Photo by Scott Olson/Getty Images)
Developer Donald Trump displays a copy of his net worth during his announcement that he will seek the Republican nomination for president, Tuesday, June 16, 2015, in the lobby of Trump Tower in New York. (AP Photo/Richard Drew)
Republican presidential hopeful Donald Trump gives a thumbs up before boarding his campaign plane to depart from Laredo, Texas, Thursday, July 23, 2015. (AP Photo/LM Otero)
AYR, SCOTLAND - JULY 30: Republican Presidential Candidate Donald Trump visits his Scottish golf course Turnberry with his children Ivanka Trump and Eric Trump on July 30, 2015 in Ayr, Scotland. Donald Trump answered questions from the media at a press conference. (Photo by Jeff J Mitchell/Getty Images)