The flap over presidential candidate and Sen. Ted Cruz's (R-Texas) Canadian birth could prove significant in the nation's first-voting state, according to a new survey from the Democratic firm Public Policy Polling.
The poll, which was shared with Business Insider ahead of its release Tuesday, found a tight Republican race in Iowa, which will hold the nation's first caucuses early next month. Real-estate magnate Donald Trump held a 28% to 26% lead over Cruz.
The new survey found that only 46% of likely Iowa Republican caucus-goers realize that Cruz was born outside the US. (More Iowa Republicans believe Cruz was born in the US than President Barack Obama.)
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FORT WORTH, TX - FEBRUARY 26: Republican presidential candidate Donald Trump speaks at a rally at the Fort Worth Convention Center on February 26, 2016 in Fort Worth, Texas. Trump is campaigning in Texas, days ahead of the Super Tuesday primary. (Photo by Tom Pennington/Getty Images)
TOPSHOT - Republican presidential candidate Donald Trump gestures during a campaign rally in North Charleston, South Carolina, February 19, 2016. / AFP / JIM WATSON (Photo credit should read JIM WATSON/AFP/Getty Images)
Republican presidential candidate businessman Donald Trump gestures during the Republican Presidential Debate, hosted by CNN, at The Venetian Las Vegas on December 15, 2015 in Las Vegas, Nevada. AFP PHOTO/ ROBYN BECK / AFP / ROBYN BECK (Photo credit should read ROBYN BECK/AFP/Getty Images)
Republican presidential candidate Donald Trump speaks during a campaign rally in North Charleston, South Carolina, February 19, 2016. / AFP / JIM WATSON (Photo credit should read JIM WATSON/AFP/Getty Images)
RENO, NV - JANUARY 10: Republican presidential candidate Donald Trump holds a campaign rally at the Reno Event Center on January 10, 2016 in Reno, Nevada. Donald Trump continued to raise doubts Sunday about rival Ted Cruzs eligibility for the presidency, saying Republicans will risk losing a lawsuitand potentially the nations highest officeif they nominate Cruz as their candidate.
(Photos by Charles Ommanney/The Washington Post via Getty Images)
MESA, AZ - DECEMBER 16: Republican presidential candidate Donald Trump speaks to guest gathered during a campaign event at the International Air Response facility on December 16, 2015 in Mesa, Arizona. Trump is in Arizona the day after the Republican Presidential Debate hosted by CNN in Las Vegas, Nevada. (Photo by Ralph Freso/Getty Images)
Republican Candidate Donald Trump arrives to speaks to the press with Rev. Darrell Scott(R), senior pastor of the New Spirit Revival Center in Cleveland Heights after meetings with prominent African American clerics at Trump Tower in New York November 30 ,2015. AFP PHOTO / TIMOTHY A. CLARY / AFP / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)
COLUMBUS, OH - NOVEMBER 23: Republican presidential candidate Donald Trump addresses supporters during a campaign rally at the Greater Columbus Convention Center on November 23, 2015 in Columbus, Ohio. Trump spoke about immigration and Obamacare, among other topics, to around 14,000 supporters at the event. (Photo by Ty Wright/Getty Images)
DORAL, FL - OCTOBER 23: Republican presidential candidate Donald J. Trump attends a campaigns rally In Florida at the Trump National Doral on October 23, 2015 in Doral, Florida. Trump leads most polls in the race for the Republican presidential nomination. (Photo by Johnny Louis/FilmMagic)
COLUMBIA, SC - SEPTEMBER 23: Republican presidential candidate Donald Trump leaves a campaign event September 23, 2015 in Columbia, South Carolina. Earlier today, Trump tweeted 'FoxNews has been treating me very unfairly & I have therefore decided that I won't be doing any more Fox shows for the foreseeable future.' (Photo by Sean Rayford/Getty Images)
NEW YORK, NY - JULY 22: Donald Trump greets supporters, tourists and the curious after taping an interview with Anderson Cooper at a Trump owned building in mid-town Manhattan on July 22, 2015 in New York City. Trump, who is running for president on a Republican ticket, has come under intensifying criticism for his behavior on the campaign trail. The billionaire's most recent comments on Senator John McCain's war record in Vietnam have resulted in almost universal criticism from fellow candidates. (Photo by Spencer Platt/Getty Images)
Donald Trump, president and chief executive of Trump Organization Inc. and 2016 Republican presidential candidate, left, looks on as Sam Clovis, newly appointed national co-chairman of Trumps campaign, speaks during a news conference ahead of a rally at Grand River Center in Dubuque, Iowa, U.S., on Tuesday, Aug. 25, 2015. President Barack Obama's top business ambassador dismissed Trump's call for a wall along the Mexico border, saying the U.S. is focused instead on expanding business with one of its biggest trade partners. Photographer: Daniel Acker/Bloomberg via Getty Images
BILOXI, MS - JANUARY 02: Republican presidential frontrunner Donald Trump pauses with supporters after speaking at the Mississippi Coast Coliseum on January 2, 2016 in Biloxi, Mississippi. Trump, who has strong support from Southern voters, spoke to thousands in the small Mississippi city on the Gulf of Mexico. Trump continues to split the GOP establishment with his populist and controversial views on immigration, muslims and some of his recent comments on women. (Photo by Spencer Platt/Getty Images)
LAREDO, TEXAS - JULY 23: Republican Presidential candidate and business mogul Donald Trump talks to the media at a press conference during his trip to the border on July 23, 2015 in Laredo, Texas. Trump's recent comments, calling some immigrants from Mexico as drug traffickers and rapists, have stirred up reactions on both sides of the aisle. Although fellow Republican presidential candidate Rick Perry has denounced Trump's comments and his campaign in general, U.S. Senator from Texas Ted-Cruz has so far refused to bash his fellow Republican nominee. (Photo by Matthew Busch/Getty Images)
DES MOINES, IA - AUGUST 15: Republican presidential candidate Donald Trump eats a pork chop on a stick and gives a thumbs up sign to fairgoers at the Iowa State Fair on August 15, 2015 in Des Moines, Iowa. Presidential candidates are addressing attendees at the Iowa State Fair on the Des Moines Register Presidential Soapbox stage and touring the fairgrounds. The State Fair runs through August 23. (Photo by Win McNamee/Getty Images)
CLEVELAND, OH - AUGUST 06: Republican presidential candidates Donald Trump (R) and Wisconsin Gov. Scott Walker participate in the first prime-time presidential debate hosted by FOX News and Facebook at the Quicken Loans Arena August 6, 2015 in Cleveland, Ohio. The top-ten GOP candidates were selected to participate in the debate based on their rank in an average of the five most recent national political polls. (Photo by Chip Somodevilla/Getty Images)
OSKALOOSA, IA - JULY 25: Republican presidential hopeful businessman Donald Trump speaks to guests gathered for a rally on July 25, 2015 in Oskaloosa, Iowa. During his last visit to the state Trump sparked controversy when he said Senator John McCain (R-AZ), a former POW, was not a war hero. (Photo by Scott Olson/Getty Images)
TURNBURRY, SCOTLAND - JUNE 08: Donald Trump Visits Turnberry Golf Club, after its $10 Million refurbishment, on June 8, 2015 in Turnberry, Scotland. (Photo by Ian MacNicol/Getty Images)
DERRY, NH - AUGUST 19: U.S. Republican presidential candidate Donald Trump hugs an American flag as he takes the stage for a town hall meeting in Derry, New Hampshire, August 19, 2015. (Keith Bedford/The Boston Globe via Getty Images)
DES MOINES, IOWA - AUGUST 15: Donald Trump at the Iowa State Fair on August 14, 2015 in Des Moines, Iowa. The Iowa State Fair is one of the oldest and largest agricultural and industrial expositions in the United States. The annual fair, the largest event in Iowa, attracts over a million visitors each year. The fair runs through August 23. After a brief walk around its time for Mr Trump to board his club cart again and leave the fair. (Photos by Charles Ommanney/The Washington Post via Getty Images)
AYR, SCOTLAND - JULY 30: Republican Presidential Candidate Donald Trump visits his Scottish golf course Turnberry 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)
TURNBURRY, SCOTLAND - JUNE 08: Donald Trump visits Turnberry Golf Club, after its $10 Million refurbishment on June 8, 2015 in Turnberry, Scotland. (Photo by Ian MacNicol/Getty Images)
Donald Trump, president and chief executive of Trump Organization Inc. and 2016 U.S. presidential candidate, gestures while speaking during The Family Leadership Summit in Ames, Iowa, U.S., on Saturday, July 18, 2015. The sponsor, The FAMiLY LEADER, is a 'pro-family, pro-marriage, pro-life organization which champions the principle that God is the ultimate leader of the family.' Photographer: Daniel Acker/Bloomberg via Getty Images
PASADENA, CA - JANUARY 16: Donald Trump arrives at NBCUniversal's 2015 Winter TCA Tour - Day 2 at The Langham Huntington Hotel and Spa on January 16, 2015 in Pasadena, California. (Photo by Angela Weiss/Getty Images)
Donald Trump, president and chief executive officer of Trump Organization Inc. and 2016 Republican presidential candidate, pauses while speaking during a news conference at Trump Towers in New York, U.S., on Thursday, Sept. 3, 2015. 'I have signed the pledge,' he said, referring to a document stating that he would not run as an independent candidate in the event that he does not win the Republican nomination. Photographer: Victor J. Blue/Bloomberg via 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)
EDISON, NJ - AUGUST 30: A golf fan takes a 'selfie' with presidential candidate Donald Trump during the final round of The Barclays at Plainfield Country Club on August 30, 2015 in Edison, New Jersey. (Photo by Ross Kinnaird/Getty Images)
ABERDEEN, SCOTLAND - JULY 10: Donald Trump plays a round of golf after the opening of The Trump International Golf Links Course on July 10, 2012 in Balmedie, Scotland. The controversial Â£100m course opens to the public on Sunday July 15. Further plans to build hotels and homes on the site have been put on hold until a decision has been made on the building of an offshore windfarm nearby. (Photo by Ian MacNicol/Getty Images)
BIRCH RUN, MI - AUGUST 11: Republican presidential candidate Donald Trump speaks at a press conference before delivering the keynote address at the Genesee and Saginaw Republican Party Lincoln Day Event August 11, 2015 in Birch Run, Michigan. This is Trump's first campaign event since his Republican debate last week. (Photo by Bill Pugliano/Getty Images)
BOCA RATON, FL - APRIL 16: Billionaire Donald Trump speaks to a crowd at the 2011 Palm Beach County Tax Day Tea Party April 16, 2011 at Sanborn Square in Boca Raton, Florida. Trump is considering a bid for the 2012 precidency and is expected to announce his running in the coming weeks. (Photo by John W. Adkisson/Getty Images)
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But just 32% of GOP caucus-goers said that someone born outside the US should be allowed to serve as president, while 47% think such a person should not be able to serve as president.
Among the latter group of caucus-goers, Trump crushes Cruz by a 40% to 14% margin.
"Our poll findings show the Birther Issue could actually cost Cruz Iowa," Tom Jensen, Public Policy Polling's director, told Business Insider in an email.
Overall, when respondents were told that Cruz was born in Canada, the vast majority — 65% — said it wouldn't make a difference in whether they support him or not. But 24% said it makes them less likely to vote for Cruz. Jensen argued that in such a close race, "that could end up being a difference maker."
Trump began talking about the issue after being asked about it during a Washington Post interview last Monday, in which he responded by saying that it could be a "precarious" issue for Republicans. Since then, Trump has mentioned it frequently in stump speeches and media appearances.
"In the case of Ted, he has to figure it out," he said. "Now, I think he can go in for some kind of a judiciary proceeding. Look, it doesn't matter what he does. You can't have a nominee who's going to be subject to be thrown out as the nominee. You just can't do it."
The Public Policy Polling survey is one of several that has shown Trump closing the gap with his now-chief rival in Iowa, after Cruz surged ahead of Trump there recently. Trump also held a two-point lead over Cruz in a Quinnipiac University survey of the state released Monday.
Trump and Cruz are in a dominant position compared to the rest of the field. The PPP poll found Sen. Marco Rubio (R-Florida) in third place at 13%. Retired neurosurgeon Ben Carson was in fourth at 8%, while former Florida Gov. Jeb Bush (R) was in fifth place at 6%.
Trump does have another potential advantage over Cruz: Less than three weeks before the caucuses, 73% of his voters said they're "committed" to voting for him, the highest percentage of any Republican. Just 58% said the same about Cruz.