House GOP leaders are moving to avoid a big end-of-year spending showdown with Democrats over national security by putting forth a bipartisan plan that would make it tougher for some foreigners to travel to the U.S. without a visa.

The legislation, aimed at overhauling the visa waiver program in the wake of the Paris terrorist attacks, is expected to be rolled out this week ahead of a vote early next week.

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It may also be included in the omnibus spending bill Congress needs to pass by Dec. 11 to avert a government shutdown, senior GOP lawmakers and aides told The Hill.

Attaching the visa bill to the $1.1 trillion must-pass spending package likely means Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE’s (R-Wis.) leadership team will skip over efforts to insert into the omnibus other security-related bills that are opposed by President Obama, including one tightening screening for refugees.

“We need to solve problems, we need to fix issues and we need to win when we pick fights,” Rep. Martha McSally Martha Elizabeth McSallyTumultuous court battle upends fight for Senate Grassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee The Hill's Campaign Report: Biden goes on offense MORE (R-Ariz.), the nation’s first female combat pilot and a member of the Homeland Security and Armed Services committees, told The Hill. “We need to get things across the finish line, through the House and Senate and signed by the president to actually fix a problem.”

GOP leaders are coalescing around the bill because it’s expected to have broad backing from both Republicans and Democrats and is seen as something that could win Obama’s signature. In a letter to the Republican whip team on Monday, GOP leaders signaled they expect the spending bill to move with bipartisan support and that they do not expect to win over every member of their conference.

Republicans believe a successful House vote on a standalone visa bill would send a message to voters that the GOP-controlled Congress is prioritizing national security and taking recent terrorism threats seriously. Including it in the larger spending bill would make national security a central component of the last measure the House is expected to approve this year.

The Obama administration itself has acknowledged the program poses security vulnerabilities; the White House on Monday rolled out several unilateral changes to better identify individuals who seek to harm the U.S.

Sens. Dianne Feinstein (D-Calif.) and Jeff Flake (R-Ariz.) introduced a similar bill Tuesday, lending more bipartisan support to the strategy. Under the current waiver program, 20 million visitors per year travel to the U.S. from 38 partner countries.

The House package would lean heavily on recommendations from a recent Homeland Security Committee task force report focused on travel by terrorists and foreign fighters. Among the proposals: requiring each country participating in the visa waiver program to issue “e-passports” with chips and biometrics and to report and monitor lost or stolen passports.

After terrorists aligned with the Islamic State in Iraq and Syria (ISIS) killed 130 people in Paris, House Republicans had initially pushed legislation strengthening the screening process for refugees fleeing violence in Syria and Iraq. Sponsored by Rep. Mike McCaul (R-Texas), chairman of the Homeland Security Committee, that bill passed the House last month with support from 47 Democrats.

But Obama has threatened to veto the proposal, and top Democratic leaders –– who opposed the measure on the House floor –– are warning that it's one of the poison-pill provisions that would threaten a government shutdown.

The omnibus debate is the latest challenge for Ryan, who could find himself facing the same dilemma that led to the ouster of his predecessor, former Speaker John Boehner (R-Ohio).

Conservatives had long-accused Boehner of caving to Obama in big policy fights rather than fighting harder for Republican ideals. And Ryan will confront similar pressures in the battle over controversial riders that Obama would likely veto.

If Ryan demands that certain riders be included, he'll satisfy his right flank but risks a government shutdown, which damaged the GOP brand in 2013. If he drops the amendments, he can avoid a shutdown but risks reprisal from the same conservatives who toppled Boehner.

Highlighting that dilemma, some Republicans will say the visa bill doesn’t go far enough. Rep. Brian Babin (R-Texas) has written a letter to Ryan, signed by more than 70 GOP colleagues, calling for a legislative “rider” in the spending bill that targets funding of the refugee program.

And McCaul, who backs the visa bill, still hasn’t given up on attaching his refugee bill to the omnibus given the president’s veto threat. Senate Majority Leader Mitch McConnell (R-Ky.) told reporters Tuesday the refugee issue is “likely to be dealt with in some way” in the omnibus, though the House will vote first.

A broader policy discussion on a range of omnibus riders will take place during a House GOP conference meeting Thursday morning.

“I don’t want to get out in front of leadership, but I’m sure [my bill] will be one of the discussions we will have Thursday morning,” McCaul told The Hill.

Still, other conservatives signaled support for the emerging Ryan strategy — partly by noting that the more immediate security threat underlined by the Paris talks is that terrorists from European countries, not refugees from Syria, could attack the United States.

Rep. Jeb Hensarling Thomas (Jeb) Jeb HensarlingLawmakers battle over future of Ex-Im Bank House passes Ex-Im Bank reboot bill opposed by White House, McConnell Has Congress lost the ability or the will to pass a unanimous bipartisan small business bill? MORE (R-Texas) said that, while the talks are ongoing, “the focus is now on the visa waiver program.”

“Most members believe that serious attention has to be paid there,” he said after emerging from a meeting of top committee chairmen. “Most members know that, in many respects, that represents even a greater threat than what we might see in the refugee program. But they all have to be addressed.”

While leaders from both parties don’t seriously believe there will be a government shutdown this month, negotiators are certain to encounter a number of hiccups in the coming days. Republicans have a wish list of riders they want to include in the spending bill, including conservative provisions targeting ObamaCare, as well as EPA and financial regulations.

House Minority Whip Steny Hoyer Steny Hamilton HoyerOn The Money: Powell, Mnuchin stress limits of emergency loans | House seeks to salvage vote on spending bill | Economists tell lawmakers: Kill the virus to heal the economy House moves toward spending vote after bipartisan talks House Democrats mull delay on spending bill vote MORE (D-Md.) said the discussion over riders has primarily been limited to the appropriations panels. But with the clock ticking down to the Dec. 11 deadline, the debate is soon to move to the leadership level.

“We'll get to some point in time, hopefully pretty soon, where the leadership will say, 'Look, this does not work for us on our side.' And they will say, 'OK, we won't pursue it on this [package],’ ” Hoyer said.

He also praised Obama for tackling the visa-waiver system –– which governs many thousands more people than the refugee program –– and said he's been in recent discussions with Republicans about how to move it through the House.

“We're talking about hundreds of thousands of visa waivers,” Hoyer said. “We ought to look at that.”