House Republican leaders on Thursday unveiled a proposal to overhaul a visa waiver program being scrutinized following the Paris terror attacks, pledging to bring it up for a vote next week and predicting it will receive overwhelming bipartisan support.

But the measure has key differences with a Senate proposal that will have to be worked out before Congress can clear legislation both parties agree is critical.

House leaders said that in addition to moving the bill as a standalone piece of legislation, which is expected to be voted on Tuesday, they also are considering including it in the year-end omnibus spending package that needs to be cleared by Dec. 11 to avoid a government shutdown.

“I want this bill to become law, any avenue to become law — as fast as possible, we’ll take it,” House Majority Leader Kevin McCarthy (R-Calif.) said Tuesday at a news conference.

The House bill is a product of negotiations conducted by a task force of committee chiefs convened in the wake of the Paris terror attacks. It aims to give the government more opportunities to screen visitors entering the country under the visa waiver program, which was created in the 1980s to streamline travel to the United States and boost tourism. Currently, passport holders of 38 countries – 30 of them in Europe – are eligible to take advantage of the reduced-screening system that allows them to visit the United States for 90 days without a visa.

Like the Senate bill drafted by Sens. Dianne Feinstein (D-Calif.) and Jeff Flake (R-Ariz.), the House legislation would require participating countries to issue enhanced passports with chips containing a traveler’s biometric information, share information on stolen passports with Interpol and share information between countries on suspected terrorists.

But the House and Senate bills differ in how they determine which individuals are too dangerous to take advantage of the program.

The House bill would ban anyone who has traveled to Syria, Iraq, Sudan or Iran since March 1, 2011, which is when Syrian civil war started, from being able to take advantage of the program. The Senate bill only places specific limits on people who have traveled to Iraq and Syria in the last five years. Both bills contain a provision that would allow the Homeland Security Department to expand the list of restricted countries.

The Senate proposal, unlike the House bill, also would require that biometric screening of all visa waiver travelers be done before people leave their home countries.

The limitations are intended to ensure that people who traveled to places where they could have been radicalized by terrorist organizations go through a full, in-person screening before being granted permission to come to the United States.

“The challenge we have is that over 5,000 foreign fighters with passports have traveled to Syria, but then traveled back to Europe,” said House Foreign Affairs Chairman Ed Royce (R-Calif.), who is part of the task force. “We don’t want to end up fast-tracking the ability of people who have that European passport to come into the United States… and carry out the same types of attacks here that they’re planning right now in Europe.”

But the process of implementing the restrictions isn’t entirely foolproof. Individuals from visa waiver countries who have been to listed countries will be required to self-report that travel on the Electronic System for Travel Authorization application – a form any would-be visa waiver traveler has to fill out.

If an individual who has been to Syria, Iraq, Iran or Sudan during the specified time period chooses not to self-report, national security officials will have to rely on either government intelligence reports or the ability of customs officers to recognize those countries’ stamps in the traveler’s passport.

“This does not solve all the problems we have with making sure our borders are secure,” said Rep. Bob Goodlatte (R-Va.), the chairman of the House Judiciary Committee. But, he added, it would help protect the country “from those who would come in and commit mayhem.”

Lawmakers are working on other proposals to respond to the Paris attacks. Homeland Security Committee Chairman Mike McCaul (R-Texas) said the task force is working through several recommendations made earlier this year in the Foreign Fighters Task Force report, a bipartisan effort released in September.

The visa waiver program was “one of the top recommendations that we needed to fix,” McCaul said.