The Trump administration is poised to buck conservative House lawmakers on gun legislation as Congress goes about crafting a response to the deadly school shooting in Parkland, Florida.

A senior administration official told The Daily Beast on Monday that the president is unlikely to insist that any legislative package on guns include a provision that would force states to comply with concealed-carry firearm permits from outside their jurisdiction.

That provision, known as concealed-carry reciprocity, is a top demand of House Republicans and a major priority of the National Rifle Association. In fact, House GOP leaders earlier this year attached it to a bill that would have strengthened the reporting requirements for background checks on gun purchases (The measure, known as “Fix NICS,” the National Instant Criminal Background Check System, never passed the Senate). And, in the wake of Parkland, House Republican leaders have promised conservatives that they will push for it again.

“It’s critical that we address the safety needs of our law-abiding citizens from all angles, which is why [House Majority Whip Steve] Scalise (R-LA) supports keeping the Fix NICS Act and Concealed Carry Reciprocity Act coupled together, as the House already passed it last year,” Lauren Fine, a spokeswoman for Scalise, told The Daily Beast.

On Monday, White House Press Secretary Sarah Huckabee Sanders declined to say if the president would make a similar demand for concealed-carry reciprocity in the days and weeks ahead. “I know the president has been supportive of it in the past but I haven’t asked him about it recently,” she said at the daily briefing.

But a senior administration official told The Daily Beast that it wasn’t something that the White House would insist on being included in a legislative package. The official, who spoke on the condition of anonymity to talk candidly about the legislative process, noted that the Senate would almost certainly scuttle any such piece of legislation because it would require 60 votes for passage. Republicans only have 51 votes in that chamber.

“I'm not sure that's where they're going to end up,” the official said. “ I think at the end of the day, we get this done without reciprocity.”

Should the administration stick to this position, it would give the prospects of gun legislation a major boost in the Senate. A bipartisan group of members in that chamber has been building support for legislation introduced by Sens. John Cornyn (R-TX) and Chris Murphy (D-CT) that would provide incentives for states that submit information to the FBI’s National Instant Criminal Background Check System (NICS). That bill faces its own hurdles in the Senate from conservative lawmakers. But a boost from Trump would likely help it get the necessary votes.

Last week, Cornyn’s office notably sent around a Wall Street Journal op-ed that encouraged congressional Republicans to drop the concealed-carry reciprocity provision and pass the Cornyn bill as a standalone measure.

The House is an entirely different matter. GOP leadership has promised conservatives that the Cornyn legislation wouldn’t be brought up as a standalone bill. And with concealed-carry reciprocity off the table, the prospect of any legislation passing—whether it be the Fix NICS bill, raising the age for buying an assault rifle to 21, or outlawing bump-stock devices that allow a semi-automatic firearm to fire like a fully-automatic one—becomes incredibly remote, even with the surviving students of the Parkland shooting providing an unexpected amount of political momentum.

“Even though there may be eloquent victims on TV, nothing is different this time,” a House GOP aide said bluntly.

Should the White House be able to manage the difficult politics in their own party, it would still have to contend with Democrats in Congress. And there, too, the dynamics get complicated. Democratic leadership is supportive of a clean Fix NICS bill. But they also will likely push to supplement it with other gun-control measures, such as universal background checks.

“It is our hope that Republican leaders will help pass real legislation that makes a difference, rather than NRA-backed bills that make Republicans feel better without meaningfully addressing the issue of gun safety,” Senate Minority Leader Chuck Schumer (D-NY) said on Monday.