Growing momentum in the Senate for new gun control legislation has failed to flow down to the House, where just a handful of House Republicans have embraced a deal to expand background checks for firearm purchases.

Rep. Peter King (R-N.Y.) and multiple Republican members of the Pennsylvania delegation are backing a compromise brokered by the Keystone State’s Sen. Pat Toomey (R-Pa.) that advanced in the Senate on Thursday.

Yet in interviews, those lawmakers said they have had no discussions with the House GOP leadership and don’t know what the prospects for the legislation would be in a chamber dominated by conservatives.

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While party leaders have made a concerted effort to prepare their rank-and-file for a major immigration push this year, they have not done so on the gun issue.

Senior aides say the topic has rarely come up in leadership meetings, as top Republicans stick to Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE’s (R-Ohio) plan to wait on Senate action on gun control.

For a second straight day, Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE refused Thursday to commit to holding a full House vote on Senate-passed gun legislation. But he said the House would not ignore an issue thrust into the spotlight by the December shooting of 20 schoolchildren in Newtown, Conn.

“Listen, our hearts and prayers go out to the families of these victims,” Boehner said. “And I fully expect that the House will act in some way, shape or form.”

Any Senate bill, he said, would be referred first to the Judiciary Committee for hearings.

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Republican leadership aides have cautioned against the expectation of quick House action, noting that the Senate has already been working on gun legislation for nearly four months. The House, an aide said, would expect to take at least as much time.

For gun control advocates, the political atmosphere in the GOP-controlled House underscores the heavy lift even to expand background checks and crack down on gun trafficking and straw purchases, which enjoy broad public support in opinion polls.

In a press conference with Sen. Joe Manchin Joseph (Joe) ManchinSenate leaders quash talk of rank-and-file COVID-19 deal OVERNIGHT ENERGY: House Democrats tee up vote on climate-focused energy bill next week | EPA reappoints controversial leader to air quality advisory committee | Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' Senate Democrats demand White House fire controversial head of public lands agency MORE (D-W.Va.) announcing the Senate measure, Toomey said the proposal had preliminary support from a number of House Republicans.

“I know there are a substantial number of House Republicans that are supportive of this general approach,” said Toomey, a former House member. “There are definitely Republicans in the House that support this.”

But with the exception of King and Rep. Charlie Dent (R-Pa.), few had come out with public statements backing the bill, and a Boehner spokesman said he was not aware of any conversations between Toomey and the Speaker.

Rep. Mike Thompson (Calif.), the leader of the Democratic House task force on gun violence, said he and King were talking to “about seven or eight House Republicans” about the Toomey bill, which they plan to introduce in the House.

Rep. Michael Grimm (R-N.Y.), a former FBI agent representing a New York City district with a sizable law enforcement community, said he was open to new gun laws but had yet to see the proposal.

“I’m going to be reasonable,” he said. “I’m a strong supporter of the Second Amendment, but when it comes to making sure criminals aren’t getting guns, the mentally disturbed are not getting guns and that there are strict penalties for those that are committing crimes, those that illegally have guns, I’m all for that.”

“I don’t think the current system is good enough, so I think we do need to tweak the current system a little bit,” Grimm added. At the same time, he characterized himself as “pretty far to the right on the Second Amendment.”

Rep. Tom Reed (R-N.Y.), whose district is in upstate New York, took a much more skeptical view of the Toomey proposal.

“I’m very concerned that if there’s any language that infringes on the Second Amendment, I’m not very interested in supporting that type of proposal,” he said.

Like other Republicans, Reed said the focus of the debate should be more on mental health issues than gun control. The root issue of gun violence, he said, is “the person behind the gun, not the gun itself.”

In his district, Reed said he has heard much more from constituents supportive of gun rights, especially in the wake of sweeping gun control legislation passed in January by the state legislature, which he opposed.

House Democratic leaders have already begun ramping up pressure on Republicans to consider gun legislation.

"If they for a minute think they can throttle this [and] put it on the back shelf or lock it away in the back room, they're going to be incredibly surprised by what happens across this country," Thompson said.

For supporters of the Toomey-Manchin proposal, their best hope may be if Boehner decides to allow a House vote even if receives less than majority backing in his conference.

The Speaker kept that door ajar on Thursday, reiterating that he does not consider the so-called “Hastert Rule” requiring a “majority of the majority” to be an iron-clad commandment.

“It was never a rule to begin with,” said Boehner, who has allowed House Democrats to carry a handful of bills to passage since President Obama’s reelection. “And certainly my prerogative or my intention is to always pass bills with strong Republican support.”