Republican Bush says rival Rubio has 'given up'

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Republican presidential candidate Jeb Bush pressed his attack on rival Marco Rubio's record of missed Senate votes, saying it showed Rubio had "given up" on breaking through the political gridlock in Washington.

Bush questioned whether Rubio, a U.S. senator from Florida, had shown the leadership skills or level of accomplishment needed to bridge partisan divides and solve longstanding problems.

SEE ALSO: Jeb Bush vows to fight through campaign's 'bumpy time'

"In this era of gridlock, it's really hard to break through, and I think he's given up. And I think that's the wrong thing to do," Bush, a former governor of Florida, said in an interview on NBC's "Meet the Press" that aired on Sunday.

"This is about public service, about solving problems," Bush said. "I can change the culture in Washington."

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In one of the most notable exchanges in last week's Republican presidential debate, Bush criticized Rubio for missing Senate votes while campaigning and suggested he resign his seat. But Rubio punched back, accusing Bush of attacking him in an effort to right his struggling White House bid.

See photos from the Republican debate on CNBC:

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GOP Debate - 10/28
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Republican Bush says rival Rubio has 'given up'
BOULDER, CO - OCTOBER 28: Presidential candidates Ohio Governor John Kasich (L-R), Mike Huckabee, Jeb Bush, Sen. Marco Rubio (R-FL), Donald Trump, Ben Carson, Carly Fiorina, Ted Cruz (R-TX), New Jersey Governor Chris Christie, and Sen. Rand Paul (R-KY) pose for a photo at the CNBC Republican Presidential Debate at University of Colorado's Coors Events Center October 28, 2015 in Boulder, Colorado. Fourteen Republican presidential candidates are participating in the third set of Republican presidential debates. (Photo by Andrew Burton/Getty Images)
Ben Carson watches as Donald Trump takes the stage during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Ben Carson, right, watches as Donald Trump speaks during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
BOULDER, CO - OCTOBER 28: Presidential candidates Ohio Governor John Kasich (L-R), Mike Huckabee, Jeb Bush, Sen. Marco Rubio (R-FL), Donald Trump, Ben Carson, Carly Fiorina, Ted Cruz (R-TX), New Jersey Governor Chris Christie, and Sen. Rand Paul (R-KY) take the stage at the CNBC Republican Presidential Debate at University of Colorados Coors Events Center October 28, 2015 in Boulder, Colorado. Fourteen Republican presidential candidates are participating in the third set of Republican presidential debates. (Photo by Justin Sullivan/Getty Images)
Republican presidential candidate, businesswoman Carly Fiorina speaks during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Jeb Bush, center, stands with Mike Huckabee, left, and Marco Rubio during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Chris Christie, left, and Donald Trump talk during a break in the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Ben Carson, right, watches as Donald Trump speaks during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
John Kasich, left, and Donald Trump, second from right, argue across fellow candidates during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Carly Fiorina, center, speaks as Ben Carson, left, and Ted Cruz look on during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Republican presidential candidate, Ohio Gov. John Kasich speaks during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Donald Trump smiles during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Rand Paul, right, speaks as Chris Christie looks on during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Ted Cruz, left, Chris Christie, center, and Rand Paul take the stage during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Brennan Linsley)
Republican presidential candidates, from left, John Kasich, Mike Huckabee, Jeb Bush, Marco Rubio, Donald Trump, Ben Carson, Carly Fiorina, Ted Cruz, Chris Christie, and Rand Paul appear during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Brennan Linsley)
Mike Huckabee speaks during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Marco Rubio, right, and Jeb Bush, argue a point during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
John Kasich makes a point during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Republican presidential candidate, Sen. Rand Paul, R-Ky., speaks during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
BOULDER, CO - OCTOBER 28: Presidential candidates Ohio Governor John Kasich (L-R), Mike Huckabee, Jeb Bush, Sen. Marco Rubio (R-FL), Donald Trump, Ben Carson, Carly Fiorina, Ted Cruz (R-TX), New Jersey Governor Chris Christie, and Sen. Rand Paul (R-KY) take part in the CNBC Republican Presidential Debate at University of Colorados Coors Events Center October 28, 2015 in Boulder, Colorado. Fourteen Republican presidential candidates are participating in the third set of Republican presidential debates. (Photo by Justin Sullivan/Getty Images)
Marco Rubio speaks during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
Chris Christie makes a point during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)
2016 presidential candidates Senator Marco Rubio, a Republican from Florida, left, Donald Trump, president and chief executive of Trump Organization Inc., center, and Ben Carson, former neurosurgeon, stand on stage at the start of the Republican presidential debate at the University of Colorado in Boulder, Colorado, U.S., on Wednesday, Oct. 28, 2015. Three Republican senators running for president have come out swinging against a bipartisan budget deal as an emblem of everything that's wrong in Washington, making it a likely pinata in the party's third debate Photographer: Matthew Staver/Bloomberg via Getty Images
Ted Cruz, left, Chris Christie, center, and Rand Paul take the stage during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Brennan Linsley)
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Rubio responded again on CBS's "Face the Nation" on Sunday, saying beating Democratic frontrunner Hillary Clinton was more important than missing meaningless Senate votes.

"The truth is, I don't like missing votes, but what I would really hate is to wake up on the first Wednesday of November to the news that Hillary Clinton's been elected president," Rubio said.

"Far too many votes today in the Senate are predetermined. We know what outcome's going to be. It's being done for messaging purposes, but it's never going to pass," he said.

Rubio's debate performance won praise and new momentum for a campaign that has been stuck in polls behind Republican frontrunners Donald Trump and Ben Carson.

Bush, meanwhile, has faced repeated questions since the debate about whether his White House bid can survive. He said that was part of the "tribulations" of a campaign.

"I have enough self-awareness to know that this is the bumpy time of a campaign," Bush said. "This is the process. I totally understand it, and I'm more than prepared to fight on."

Bush told NBC he had never seen a memo from his campaign that surfaced last week calling Rubio a "risky bet" for Republicans. But he said "comparing and contrasting" candidates is part of the political process.

Watch Bush's interview on 'Meet the Press' in full:

Jeb Bush Is Ready to

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