But as the debate intensifies, higher-ranking Democrats appear slightly more concerned than their rank-and-file counterparts and liberal supporters about letting Syrian refugees into America. And their public comments indicate they're at least leaving the door open to pausing it too.
Here's what Sen. Charles E. Schumer (D-N.Y.), Senate Democrats' No. 3 and the Senate Democratic leader-in-waiting, said on Tuesday afternoon:
Longtime Sen. Dianne Feinstein (D-Calif.), the ranking member of the Senate intelligence committee, warned in a statement Tuesday "we need to be very careful about Syrian refugee admissions."
The Hill reports that Sen. Joe Manchin (D-W.Va.) signed a letter to President Obama calling on him to not allow any more Syrians into the country "unless federal authorities can guarantee with 100 percent assurance they are not connected" to the Islamic State.
Amid all this, Senate Minority Leader Harry Reid (D-Nev.) said Tuesday he's talked with the White House about what, if anything, needs to be improved about the federal government's Syrian vetting process. He reiterated in a press conference that he doesn't think the process should be paused -- or at least, not yet.
"My personal feelings are I’m going to wait till tomorrow," he told reporters, referring to a briefing on how the process works scheduled for Wednesday. "I don’t think at this stage we should be pausing until we get the facts."
That's not exactly saying no.
Few Democrats have gone so far as New Hampshire Gov. Maggie Hassan, who on Monday joined Republican governors from more than half of states and said the program should be stopped in its tracks until the government can “ensure robust refugee screening."
Hassan, it should be noted, is in a tight Senate race against incumbent Sen. Kelly Ayotte (R-N.H.), who has opposed the refugee program (a smart political move for Republicans, notes The Fix's Chris Cillizza.)
Which could explain why other Democrats whose elections aren't assured are echoing similar hang-on-a-minute refrains: Nevada Democratic Senate candidate Catherine Cortez Masto -- a top hope for her party to hold Reid's seat next year -- said in a statement: "I share the concerns of some Republicans in Congress to ensure the United States Intelligence Community approves the vetting process before we accept more refugees."
In Louisiana, Democrat John Bel Edwards, who is hoping to win a runoff Saturday for governor against Republican Sen. David Vitter, said in a debate that he supports current Republican Gov. Bobby Jindal's executive order to ban Syrian refugees from being placed in the state. (Despite this, Edwards was on the receiving end of a doozy of a political ad this week about Syrian refugees, tying him to Obama.)
Back in Congress, Schumer, who represents New York City, knows all too well what Parisians are going through right now. And Manchin, coming from his red state, has been known to break with his party frequently.
In other words, many of the Democrats who have left open the idea of putting the brakes on letting 10,000 Syrian refugees into the country could have their own reasons for doing so, and the idea has hardly caught on in the party more broadly. But it's still notable that, just a day after Obama stood before the world's media and declared "slamming the door in [refugee's] faces would be a betrayal of our values," high-ranking lawmakers are on a considerably different page.
There's no doubt that America's refugee process, once a nonpartisan issue, is now an intensely political one. But while Republicans are largely in agreement about all of this, Democrats have not joined in a united front with Obama on the other side.