Rubio weighs in on calls to be Trump's running mate

Sen. Marco Rubio, R-Florida, weighs in on the Brexit vote, Donald Trump's immigration plan, and his decision to run for re-election to the Senate

Marco Rubio is running for reelection to the U.S. Senate, and he definitely isn't interested in suggestions that he would be a good choice to be Donald Trump's vice presidential running mate, he said in an interview airing Sunday.

"Yeah, well, it's too late for that," Rubio told CBS' "Face the Nation" Saturday in Miami. "I'm running for the United States Senate from Florida. And you can't run for two offices at once, so."

Pushed again on the question by moderator John Dickerson, Rubio repeated that he wouldn't be able to share a ticket with Trump. When Rubio was still a presidential hopeful, the two men frequently clashed on the campaign trail.

Rubio on Brexit and Trump: "We cannot isolate ourselves from global events"

"That's not for me a viable option. And I said that months ago," he said. "The differences in policies that me and Donald have had are too big for something like that to work. It would be a distraction quite frankly to his campaign."

Asked about the political motivations behind the United Kingdom's vote to leave the European Union last week, Rubio said many people in the world feel left behind by the 21st century "global economy."

"There is a sense in many countries around the world that this is because we're too engaged with this global economy, we're too engaged with the world," he said. "I think you see it manifested here in America. I think you saw it in that vote there. I think there's other places where you may see that pop up as well."

He said much of that same frustration is present in the U.S. electorate, which is a big part of Trump's appeal to GOP voters here.

"I mean, it's one of the fundamental arguments he's made, is that the U.S. needs to isolate itself a little bit more from some of the other things that are going on around the world and focus on America first," he said. "And there are some elements of truth to that argument. But ultimately, again, not entirely. Because given the dynamics that we now live in today, we cannot isolate ourselves from global events."

Sen. Marco Rubio: "Criminals need to be deported"

After saying during his presidential campaign he would not trust Trump with America's nuclear codes, Rubio repeatedly demurred when asked if he would trust presumptive Democratic nominee Hillary Clinton with them, though he did criticize Clinton's foreign policy worldview--referring specifically to the "reset" with Russia, the pivot to Asia and the transfer of prisoners from Guantanamo Bay.

"Well, look, I think there's a process for the presidency," he said. "And once you assume the office, no matter who holds that office, I think that the reality and the gravity of it always weighs on these people. It's a very difficult issue to face. So I would hope that I can trust no matter who wins with the nuclear codes."

As for Trump's plans if he's elected president in November, Rubio said if he's reelected to the Senate he would plan to fight several parts of Trump's agenda--including his Muslim immigration ban and his plan to deport 11 million illegal immigrants.

On deporting immigrants, Rubio said, "the reality of it is you can't do it."

Rubio on decision to run for Senate re-election: I'm not giving up

"You can't round up and deport 11 million people. There are people that need to be deported. Criminals need to be deported," he said. "But you can't round up and deport 11, 10, 9 million people. The American people wouldn't stand for it once they saw what it would take to make that happen."

And when it comes to Trump's proposed ban on Muslim immigration, Rubio said it's "bad policy" and he would work to push Trump in a "different direction."

"I think it's bad policy for the country to say you're going to have a religious exclusion. And I think you've heard from multiple leaders in our party say that," he said. "...The problem he's trying to deal with is radical Islamic terror. And I believe we will be able, or I hope we will be able, to encourage him in a different direction from that."

Rubio, who until recently had very adamantly insisted he would be a private citizen next year, said he decided to run for reelection because he doesn't want to "give up on it." The Florida politician has made no secret of his distaste for the Senate, and he was criticized during his presidential bid for missing votes and hearings.

Despite his frustration with the Senate, does Rubio think he can get anything done in a second term? "I hope so," Rubio said. "It's hard."

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    Emily Schultheis

    Emily Schultheis is a reporter/editor for CBS News Digital.