WASHINGTON — The bloody attacks in Paris are putting the Syrian refugee crisis at the center of U.S. politics as migrants from that war-torn country surge toward the West and security concerns rise.

The debate, which cuts straight to the American identity as a refuge, on Monday ranged from whether to only admit Syrians who are Christian to whether to close some mosques. But across the political landscape, caution intensified about vetting Syrian refugees and whether to allow them into the country at all.

GOP presidential frontrunner Donald Trump suggested in a MSNBC interview that he would “strongly consider” closing some mosques if elected. Former Florida Gov. Jeb Bush said the U.S. should focus on admitting Christians. And GOP presidential contender Marco Rubio for the first time said the United States should no longer accept Syrian refugees because it’s impossible to know whether they have links to Islamic militants — an apparent shift from earlier statements in which he left open the prospects of migrants being admitted with proper vetting.

“It’s not that we don’t want to, it’s that we can’t,” Rubio said Sunday on ABC’s “This Week.” “Because there’s no way to background check someone that’s coming from Syria.  Who do you call and do a background check on them?”

Bush said Syrian Christians should be admitted to the U.S., but only after proper vetting.

“I think our focus ought to be on the Christians who have no place in Syria anymore,” he added in NBC’s “Meet the Press.” ‘’They’re being beheaded, they’re being executed by both sides.  And I think we have a responsibility to help.”

President Barack Obama condemned that approach as the opposite of American values.

“When I hear folks say that, well, maybe we should just admit the Christians but not the Muslims, when I hear political leaders suggesting that there would be a religious test for which person who’s fleeing from a war-torn country is admitted, when some of those folks themselves come from families who benefited from protection when they were fleeing political persecution, that’s shameful,” Obama said at the G-20 Summit in Antalya, Turkey. “That’s not American, it’s not who we are.”

Obama has said that the administration is moving forward with its plan to thoroughly vet and admit as many as 10,000 Syrian refugees. All three Democratic presidential candidates have said they would admit Syrians but only after thorough background checks.

But Friday night’s mass killings in Paris, which left at least 129 people dead, offered evidence that may have backed up what many had been warning: People with secret ties to Islamic militants could flow across borders as part of waves of refugees.

Authorities said a Syrian passport found near one of the Paris attackers that had been registered last month and traveled through three countries along a busy migrant corridor known for lax controls. It was not clear whether the document was real or forged. Officials on Sunday were still trying to identify people involved in the conspiracy. They said as many as three of the seven suicide bombers who died in the attacks were French citizens.