Sen. Susan Collins and her fellow senators supporting a compromise proposal to make it tougher for terror suspects to buy guns have some work on their hands.  

The Maine Republican earned praise from both sides of the aisle for stepping up to find consensus, unveiling her proposal to the press with bipartisan supporters by her side after Tuesday’s caucus lunches.  

Sen. Christopher S. Murphy, the Connecticut Democrat who has emerged as a leader in the gun-control debate , called it a “watershed moment.”  

“I think you are seeing in real time the vise grip of the NRA loosening on this place,” he said.  

But the National Rifle Association is decidedly against the mechanism to keep people on some terror watch lists from buying guns, questioning the constitutionality of that approach.  

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And the Obama administration is reviewing the bill with an eye toward whether it would complicate the Justice Department’s work.  

Beyond that, Democrats and Republicans — who voted down each other’s amendments on guns and terror suspects on Monday — are watching to see what the other side will do.  

Sen. Charles E. Schumer, D-N.Y., said he would like to see Republicans support the proposal that he dubbed the “Buck the NRA Bill.”  

“It’ll be the first time that in a bipartisan way, with significant Republican support, the NRA was told, ‘You’re way off base, Americans need to be safe. We’re going to work together,'” he said.  

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Senate Majority Whip John Cornyn, R-Texas, said Collins will need Democratic support for her effort to succeed.  

“I think it remains to be seen whether Democrats who had previously criticized the approach are now willing to support it, and whether those who are concerned about due process on the front end, not on the back end, will support it,” Cornyn said.  

Following the June 12  terror shooting in Orlando that left 49 people dead, Congress has been working to find the right response. A Democratic filibuster last week led to votes on the Senate floor on Monday, including on a Democratic amendment banning gun sales for everyone on the government’s terror watch lists and a Republican proposal for a three-day waiting period.  

After both were blocked, Collins, R-Maine, moved ahead with the Terrorist Firearms Prevention Act of 2016 to bar firearms from being sold to individuals on what are known as the “selectee” and “no fly” lists, rather than the considerably larger “Consolidated Terror Watch List.” The “selectee” list includes the names of those singled out for extra screening at airports.  

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Her co-sponsors on the measure include: Democratic Sens. Heidi Heitkamp of North Dakota, Martin Heinrich of New Mexico and Tim Kaine of Virginia. Republican backers include Kelly Ayotte of New Hampshire, Jeff Flake of Arizona and Lindsey Graham of South Carolina. Angus King, a Maine independent, is also co-sponsoring the bill.  

Flake said the work started after Collins spoke at an internal Republican meeting last week about finding an alternative to the competing proposals from Cornyn and Democratic Sen. Dianne Feinstein of California.  

“Many of us were uncomfortable with the amendments that seemed to be put up destined to fail and we wanted one that could actually pass,” Flake said. “Sen. Collins mentioned in the meeting that we had that we ought to narrow it down to the no-fly and selectee list and put in robust due-process things. I went up to her and said, ‘Let’s work.'”  

Collins said she exchanged roughly 30 text messages and calls with the Democrats Heinrich and Heitkamp of North Dakota in crafting the proposal.  

Heitkamp was speaking with Democratic colleagues about the plan at Tuesday’s caucus lunch, and there were initial signs that Democrats could rally behind it if concerns raised by the Justice Department can be addressed without losing Republican votes.  

Feinstein, who sponsored the Democratic amendment that failed Monday, said Tuesday that while the Collins proposal comes up short of her preferred legislation, it was too early to say if she could support it.  

“We’d like to be able to have something pass. I spoke to Senator Collins. My staff are going to meet with her. We’ve gone over her bill now. We believe there are at least four or five changes that need to be made just to conform with concerns of the Justice Department, so we’re going to try and see if that can’t get done,” Feinstein said.  

The Obama administration said it was holding off on backing the measure, since White House and Justice Department lawyers were still studying it.    

On the Republican side, many of the skeptics cite constitutional, due process concerns.  

The measure provides for a process for individuals to go to court to appeal their presence on the selectee and no-fly lists, and while there would be a process for recouping attorneys fees, that would come into play after they were not allowed to buy a gun.  

Cornyn raised due process concerns, and so did the NRA.  

“Keeping guns from terrorists while protecting the due process rights of law-abiding citizens are not mutually exclusive,” NRA executive director Chris W. Cox said in a statement. “Unfortunately, Senator Collins and others are focusing their efforts on unconstitutional proposals that would not have prevented the Orlando terrorist attack.”  

Some senators say they are still reviewing the proposal. “I’d like for us to do something, but it has to be something that would have prevented the attack in Orlando or a potential future attack,” said Sen. Marco Rubio, R-Fla.  

Graham challenged his colleagues.  

“If we can’t do this I don’t know what we’re ever going to do,” Graham told reporters. “And if you’re a member of the Senate, you’re betting that nobody on this list ever goes out and buys a gun and kills a bunch of people with it.”  

Bridget Bowman and Todd Ruger contributed to this report. Contact Lesniewski at NielsLesniewski@cqrollcall.com and follow him on Twitter @nielslesniewski .