Washington – U.S. Sen. Chris Murphy is among several lawmakers who are saying there is little danger to the United States from the Syrian refugee resettlement program under debate after the Paris attacks, but there are vulnerabilities in the way tourists and other visitors to the United States are processed.

The lawmakers want to reform the ‘visa waiver’ program, which allows visitors from nearly 40 U.S. allies to travel to the United States without obtaining a visa as long as they stay fewer than 90 days. The list includes most European countries, along with Australia, Chile, Japan and South Korea.

One change under consideration is that visitors be fingerprinted before they get to the United States, not when they reach U.S. shores.

Murphy, a member of the Senate Foreign Relations Committee, said the United States should also press the European Union to share information it has on its watch list so it could be added to the U.S. “no-fly” list.

“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. The Europeans have not been as generous as they could be."

The visa waiver program was inaugurated in 1986 and brings almost 20 million people to the United States every year. It is a reciprocal agreement with U.S. allies, allowing Americans to travel to visa waiver countries without having to apply for a visa.

Senators were briefed on the vetting of refugees late Thursday by Homeland Security Secretary Jeh Johnson. But Murphy said the issue of visas occupied most of the discussion.

U.S. policy to resettle Syrian refugees caught fire among Republicans in Congress after GOP governors said they would not allow them to resettle in their states. The states have no authority to bar people who are lawfully in the country, but they can refuse to cooperate with resettlement efforts.

The Republican governors were responding to reports that one of those involved in the Paris attacks last week may have posed as a Syrian refugee.

Despite a veto threat from the White House and uncertainty in the Senate, House Republicans plan a vote Thursday on a bill that would prevent Syrian and Iraqi refugees from entering the United States unless U.S. government officials verify they don’t pose a security threat.

Yet some Republicans are also saying the visa waiver program poses more risk than the Syrian resettlement program.

“I would tell you, from a threat standpoint, I’m probably more concerned with the visa waiver program today,” said Sen. Richard Burr, R-N.C., chairman of the Senate Select Committee on Intelligence. “Were I in Europe already, and I wanted to go the United States, and were I not on a watch list or a no-fly list…the likelihood is I would use the visa waiver program before I would try to pawn myself off as a refugee.”