Sen. Marco Rubio, one of a handful of lawmakers vying for the Republican presidential nomination, said Sunday he’s backing a measure in Congress that would place limits on Syrian refugees trying to enter the United States.

The Florida senator cited a lack of confidence in U.S. officials' ability to effectively vet refugees as the prime reason for his support of the bill. It passed the House this week and is headed to the Senate, where its chances are uncertain. The Obama administration has proposed admitting at least 10,000 Syrian refugees into the United States next year, but the bill would essentially halt the effort. The White House has said President Obama would veto it should it reach his desk.

“We can’t allow anyone in this country that we can’t vet,� Rubio said on "Fox News Sunday." “And I believe that the vast majority of refugees that are trying to come here are people that we will not be able to vet.�

The issue has propelled to the forefront of the presidential race in recent weeks, with Democrats and Republicans divided.

Rubio is joined by his Senate colleagues, Ted Cruz of Texas and Rand Paul of Kentucky, who are also seeking the GOP nomination, in his opposition to the allowing Syrian refugees into the country. On the Democratic side, front-runner Hillary Clinton supports the White House proposal to house refugees fleeing the war-torn country.

Rubio did offer some leeway in possibly allowing some refugees into the country.

“Does common sense still apply? Of course, it does. A 5-year-old orphan, a 90-year-old widow, a well-known Chaldean priest, these are obviously common-sense applications that you can clearly vet them just by common sense,� he said. “But what about someone who doesn’t fit that profile? There is no reliable database that we can rely on.�

In recent weeks, Rubio has surged some in his quest for the nomination. In several state polls from Iowa and New Hampshire he’s consistently improved.

However, rivals like former Florida Gov. Jeb Bush have assailed Rubio for his dismal attendance record in the Senate as he runs for president. Rubio has brush aside the criticism, noting that he's able to effectively toggle between the two tasks.

Ben Carson is appealing to evangelical voters in Iowa. On Sunday, he made the rounds at a church in Tipton, Iowa. Read this recent piece by The Times' Seema Mehta about Carson's appeal to Christian conservatives in the Hawkeye State.

Ben Carson speaking on ABC's "This Week" on Sunday. Some of his advisers say he's struggled to understand foreign policy.

Donald Trump outlined more controversial steps he would take in the name of national security if he becomes president, calling Sunday for the return of the widely discredited interrogation technique of waterboarding and repeating that he’d track Muslims and shutter mosques in the U.S.

Insisting that the United States “would have to be strong,� Trump said that waterboarding Islamic State extremists would be “peanuts� compared with the group’s beheadings of American and British hostages.

“I would bring it back. I think waterboarding is peanuts compared to what they’d do to us … what they did to James Foley when they chopped off his head,� Trump said on ABC's "This Week" referring to the American journalist beheaded by Islamic State in August 2014. “That’s a whole different level and I would absolutely bring back interrogation -- and strong interrogation.�

In the wake of the Sept. 11, 2001, attacks, the Bush administration turned to waterboarding, a method in which a suspect is made to feel like he’s drowning, to try to extract information from Al Qaeda suspects. The effort proved mostly futile in producing useful intelligence about planned attacks and led to false confessions, according to the executive summary of a long-delayed Senate report that came out late last year. President Obama formally ended the program when he took office in 2009.

Trump, though, said he sees waterboarding as a useful counterbalance to the violent murders committed by Islamic State.

“You know, they don’t use waterboarding over there; they use chopping off people’s heads,� he said.

Trump also doubled down on his calls for a database to monitor Muslims and the possibility of shuttering mosques.

At a rally in Birmingham, Ala., on Saturday, Trump again brought Muslims to the forefront – a topic he’s focused on in the aftermath of the Paris terror attacks. Trump told the estimated 10,000 people in attendance he saw images of Arab Muslims cheering in New Jersey after the Sept. 11 attacks.

“There were people that were cheering on the other side of New Jersey where you have large Arab populations,� he said on “This Week.� "They were cheering as the World Trade Center came down. I know it might be not politically correct for you to talk about it, but there were people cheering as that building came down -- as those buildings came down, and that tells you something. It was well covered at the time.�

Rumors have surfaced over the years about Muslims cheering in Paterson, N.J., as the twin towers collapsed, but those claims were discounted by local police at the time.

During the rally, a protester from the Black Lives Matter movement heckled the real-estate mogul. When asked about it in a separate interview Sunday on “Fox & Friends,� Trump suggested the protester should have been “roughed up.�

“Maybe he should have been roughed up because it was absolutely disgusting what he was doing," Trump said. “The man that was — I don't know, you say 'roughed up' — he was so obnoxious and so loud. He was screaming. I had 10,000 people in the room yesterday — 10,000 people. And this guy started screaming by himself.�

Since he entered the GOP presidential race over the summer, Trump has catapulted to the top of the crowded field, tapping into an electorate discontented with the political establishment. And with less than three months until ballots are cast, he remains toward the top of polls in the early voting states of Iowa, New Hampshire and South Carolina.

Trump also stoked fears among the Republican Party that if he does not capture the party's nomination, he will seek a third-party run for president. Though he signed a pledge months ago promising to support the Republican nominee in what was seen as something of a peace agreement between Trump and party leadership, he said Sunday that he’s still considering running as an independent.

“I will see what happens. I have to be treated fairly. You know, when I did this, I said I have to be treated fairly. If I'm treated fairly, I'm fine,� he said Sunday on “This Week.�

Republican Louisiana Gov. Bobby Jindal ended his presidential campaign last week. Stay up to date on the field of Democratic and Republican presidential hopefuls.