House Speaker Paul Ryan of Wis., left, and Senate Majority Leader Mitch McConnell of Ky. have agreed to a “full debate” on the Syrian refugee issue, which was excluded from the omnibus, next year.  (AP Photo/Andrew Harnik)

After weeks of threats, the White House avoided a GOP bid to block 10,000 Syrian refugees from entering the country in the annual spending bill.

Republicans wanted to add a measure to suspend Syrian and Iraqi refugee admissions to the year-end budget package, but were stymied by Democratic leaders, who roundly opposed it.

But Republican leaders are promising this is hardly the end of the fight.

House Speaker Paul Ryan (R-Wisc.) stressed that he had struck a gentleman’s agreement with Senate Majority Leader Mitch McConnell (R-Ky.) during budget negotiations, securing a promise that there would be a “full debate” on the refugee issue in 2016.

“The majority leader of the Senate has given us a commitment that they will address this issue early in 2016,” Ryan said at a news conference Wednesday morning. “So, the bill that we sent over there, we have a commitment from the Senate that they will bring up the refugee issue and that they will have a full debate on refugees.”

A McConnell spokesman confirmed the Senate would address Syrian refugee admissions in the first quarter of next year. But the effort will still have to overcome significant Democratic opposition to go anywhere: Senate Minority Leader Harry Reid (D-Nev.) told reporters last month that a bill to curtail Syrian refugee admissions “won’t get passed” in the Senate.

Last month, the House passed a bill — which Obama threatened to veto — to impose a temporary moratorium on Syrian and Iraqi refugee admissions until the administration met certain security benchmarks; the FBI director certifies that each refugee had passed a satisfactory background check; and Homeland Security and intelligence officials certify that refugees entering the United States would not pose a terror threat.

“This reflects our values, this reflects our responsibilities,” Ryan said of the legislation at the time. “We cannot and should not wait to act, not when our national security is at stake.”

[House passes bill to tighten flow of refugees over Obama’s objections]

Several House Republicans took that sentiment one step further, calling for the Syrian refugees issue to be included in the must-pass omnibus spending package.

Such calls gained momentum after a strong showing in the House: Forty-seven House Democrats voted for the House bill to require more stringent security standards to admit Syrian and Iraqi refugees, giving it a veto-proof majority in the process.

In the weeks since, more than half of those Democrats signed on to a letter asking that refugees be left out of the spending package. And a few leading Republicans, such as Sen. John McCain (R-Ariz.), warned that it was not worth risking shutting down the government to secure a refugee rider.

But for some Republicans, the absence of Syrian refugee language in the omnibus is a real problem.

Rep. Lou Barletta (R-Pa.), who advocated withholding money from agencies that process Syrian refugees, said the omission was “a major sticking point” for him.

“Syrian refugees is an issue that I feel very strongly about,” Barletta said. “That was the one issue that was really a priority.”

Republicans promoting the omnibus are trying to rally the troops by pointing to limits on the waiver program included in the final bill. The spending package incorporated a measure from Rep. Candice Miller (R-Mich.) updated after review by a task force of Republican committee chairmen convened in the wake of the Paris attacks. That measure passed the House by a vote of 407 to 19 earlier this month.

House Appropriations Committee Chairman Hal Rogers (R-Ky.) counted the inclusion of the visa waiver bill in the omnibus package as one of the Republicans’ biggest wins, along with ending the ban on oil exports.

[Here’s what made it into the omnibus]

But there are also lingering concerns about that legislation primarily from Democrats.

Several lawmakers take issue with the limitations on individuals who are dual nationals of countries eligible to participate in the waiver program, as well as citizens of Syria, Iraq, Iran and Sudan. Under the bill, passport holders from waiver countries who are either nationals of or have traveled to those countries since March 1, 2011, are not eligible to take advantage of the program. Instead, they would have to apply for a visa through the normal processes, including an in-person interview at an embassy or consulate.

But many lawmakers feel the restriction is unfair to the many nationals who inherited their second nationality by ancestry or familial ties, even if they have never set foot in one of the countries requiring additional review.

A couple dozen House Democrats signed a letter urging Senate leaders to amend the House-passed bill to prohibit dual nationals of Syria, Iraq, Iran and Sudan from using the waiver program. They want to establish exceptions for aid workers, journalists, and researchers who have traveled to those countries, and require reauthorization for program changes.

Senate Foreign Relations Committee Ranking Member Ben Cardin (D-Md.) sent another letter to House and Senate leaders, warning that including the waiver measure in the omnibus was “likely to trigger reciprocal treatment of similar U.S. citizen dual nationals.”

Many lawmakers pledged to further examine how foreign nationals enter the U.S.  But there are no firm plans to reexamine the waiver program right now.

Some members would like to revisit the waiver legislation.

Senate Intelligence Committee Ranking Member Dianne Feinstein (D-Calif.) said Wednesday that she wanted “to improve the program, including looking at ways to collect biometrics from first-time visa waiver travelers before they depart their home countries.”

In the House, Intelligence Committee Ranking Member Adam Schiff (D-Calif.) said he hoped Congress could “fix” the dual citizen provisions.

“In particular cases where someone has never been to Syria and Iraq, that’s something we should be able to clean up,” Schiff said.