Rubio also defended the nasty rhetoric of the Republican presidential debate in an interview with CNN's Dana Bash held in front of a live audience at the Conservative Political Action Conference and aired Sunday on "State of the Union."
"I don't want us to have a president that we constantly have to be explaining to our kids, 'Look, I know that's what the president did, but you shouldn't do that.' I don't want that," Rubio said.
"Donald Trump -- he might have grown up the way he did, with a lot of money and going to boarding school. I can tell you this: Where I grew up, if someone keeps punching people in the face, eventually someone's going to have to stand up and punch them back," he said.
The Florida senator wouldn't say whether he has asked former Florida Gov. Jeb Bush -- a one-time presidential rival -- for his endorsement ahead of Florida's 99-delegate, winner-take-all primary.
But he did say he expects to win the state, and he harkened back to his 2010 Senate race against then-Gov. Charlie Crist.
Rubio said he has "never based his campaign on one state, but we will win the state of Florida."
"We will beat Donald Trump there the way we beat Charlie Crist," he said. "I have experience beating people who say they aren't who they truly are."
Rubio was in front of an audience that was receptive to his shots at Trump.
He mocked the Republican front-runner for canceling his planned appearance at CPAC, referring to the host organization and saying, "this is the American Conservative Union, and so it's usually reserved for conservatives."
Rubio also defended his decision to wait until recent weeks to unload a series of attacks on Trump's style, business dealings and more.
"I didn't get into this to beat up on other candidates, I really didn't," Rubio said. He ticked off Trump's positions on Planned Parenthood, Israel and health care -- and added that a year ago, he'd have wondered, "on what planet would that be the Republican front-runner?"
During the interview, Rubio also pledged he wouldn't nominate anyone for the Supreme Court in the last year of his tenure in the Oval Office if he's elected -- saying that President Barack Obama shouldn't fill deceased Justice Antonin Scalia's seat.