While Syrian refugee resettlement has dominated the headlines in Congress this week, the more pressing national security debate in the Senate is about the way tourists and other travelers enter the United States.  

Senators from both sides of the aisle emerged from closed briefings concerned about security risks posed by the visa waiver program, which allows citizens from 38 countries to visit the U.S. for up to 90 days without a visa. After an all-senators briefing by administration officials late Wednesday afternoon, Sen. Dianne Feinstein, D-Calif., said she intends to introduce legislation Thursday — along with Sen. Jeff Flake, R-Ariz. — that would bar individuals who have been in Syria or Iraq within the past five years from making use of the visa waiver program to gain entry into the U.S.  

Sen. Christopher S. Murphy, D-Conn., said visas occupied more of the discussion in the briefing with Homeland Security Secretary Jeh Johnson and other top officials than did refugee vetting. The Foreign Relations panel member expressed particular concern about those carrying European passports.  

“I think this is the moment to make sure that Europe is serious about populating their watch list in a way that protects the United States through the visa waiver program,” Murphy said. “Our visa waiver program is only so good as our no-fly list. And our no-fly list is only as good as the information that the Europeans give us.”  

Sen. Rand Paul, R-Ky., a presidential hopeful, was already proposing a new waiting period for individuals entering the U.S. from places such as Belgium and France, even before the administration briefing.  

“In my bill, we see that you have to either come through Global Entry or you have to wait 30 days, and I have a feeling that some of the people who are part of that attack could have gotten on a plane and come to the United States,” Paul said in an interview. “So, I think we have to have more checks in place. I asked for many of these things during the immigration battle.”  

Coming out of a Wednesday morning closed-door briefing, Foreign Relations Chairman Bob Corker told reporters that security risks associated with the visa waiver program have “caused some degree of concern.” The Tennessee Republican was standing in roughly the same spot where, a day earlier, Intelligence Chairman Richard M. Burr signaled the visa waiver system might be the easiest way for a would-be terrorist to enter the U.S.  

“Were I in Europe already, and I wanted to go to the United States and I was not on a watch list or a no-fly list and I wanted to get there, the likelihood is I’d use the visa waiver program before I would try to pawn myself off as a refugee,” the North Carolina Republican said.  

The apparent focus on the visa waivers does not mean the Senate won’t tackle ongoing concerns about the identification and vetting of Syrian refugees. The House will vote on a bill Thursday to enhance oversight of the screening process for refugees from Syria and Iraq.  

Majority Whip John Cornyn, R-Texas, said the visa waiver program had long been a concern that was only heightened by the Paris attacks, but he was more focused on the vetting process for Syrian refugees — as many as 10,000 of whom are expexted to enter the country over the next year.  

“The most troubling thing I’ve heard so far is the FBI director saying if these refugees aren’t in the database, then there’s nothing to vet and there’s no information that would give you any indication about potential security issues,” Cornyn said. “I think it’s kind of a practical problem as well as a philosophical or ideological problem.”  

But visa questions did also come up at a Senate Republican lunch Wednesday, where Sen. Dan Coats, R-Ind., re-upped a legislative proposal that includes Homeland Security overhaul requirements of the program and terminates the special status for uncooperative countries.  

Still, the discussion about how to further secure the program comes as Sens. Mark S. Kirk, R-Ill.; Barbara A. Mikulski, D-Md.; and others have championed an effort to expand the number of countries on the waiver list by adding Poland. The terrorist attacks in Paris may have slowed down the momentum for Poland’s inclusion on a list that already includes most European countries, along with Australia, Chile, Japan and South Korea.  

“I think it’s got to be part of the same discussion, and you know there are considerable advantages to the visa waiver program in terms of visitors to this country, and we don’t want to necessarily just walk away from those benefits,” Sen. Angus King, I-Maine, said. “But in light of the way the world is working these days, it’s something we have to take a look at.”  

Ryan McCrimmon contributed to this report.