Sens. Heidi Heitkamp (D-N.D.), left, Martin Heinrich (D-N.M.) and Susan Collins (R-Maine) leave a news conference on June 21. (Evan Vucci/AP)

Sen. Susan Collins’s gun-control compromise will get a vote in the Senate this month — the only question is whether enough senators will support it.

Collins (R-Maine) and her supporters are selling their measure, which would bar roughly 2,700 Americans suspected of being terrorists from buying a gun, as the only way to break the political logjam surrounding the emotionally charged issue of gun control in the wake of violent shootings such as the one in Orlando over a week ago.

“What you see here is an effort not to have a vote that will simply allow each party to use a cudgel to beat the other party with, but rather to have something that would actually pass,” said Sen. Jeff Flake (R-Ariz.), a member of the eight-person group that has met over the past week to hash out the proposal.

Said Sen. Martin Heinrich (D-N.M.), another member of Collins’s group: “It’s very comfortable for us to sit in our respective corners and vote for something that we know isn’t going to change things. It’s time to start putting progress in front of politics.”

Collins’s proposal denies the right to purchase guns to anyone on two subsets of the FBI’s Terrorist Screening Database: the “No Fly List,” which prohibits suspected terrorists from boarding planes heading to or from the United States or crossing U.S. airspace, and the “Selectee List,” which requires extra screening procedures. There are approximately 109,000 people on those lists, including about 2,700 Americans, by the senators’ count.

“Essentially we believe that if you are too dangerous to fly on an airplane, you’re too dangerous to buy a gun,” Collins said Tuesday.

But Democrats have said Republicans need to lure about 20 votes to make passing Collins’s proposal “doable” — and that is a bar that no one is yet sure they can clear. “I think we’re getting there — I do,” Flake said.

Senate Democratic Conference Vice Chair Charles Schumer (D-N.Y.) said Tuesday that Collins’s proposal is “a step in the right direction” but that it also has “some serious problems.”

He argued that a focus on the two smaller lists would let hundreds of thousands of other suspected terrorists potentially slip through the cracks. He also said that the expedited appeals process for anyone believing they were mistakenly denied a gun is too fast.

On Monday, Sen. Dianne Feinstein (D-Calif.), who authored one of four bills that failed in the Senate this week, said that Collins’s proposal is “not enough to close the loophole that creates this terror gap.”

Democrats are predicting that they will “do more than our share on the Democratic side of the aisle,” as Heinrich said, to help pass the proposal. But he hinted that not all Democrats would be on board.

“There is a ‘let the perfect be the enemy of the good’ that exists on both sides of the aisle,” Heinrich said.

Passing gun-control legislation will be an uphill battle in the Senate, and it would face even stauncher resistance in the GOP-controlled House. Four gun-control proposals were rejected by the Senate on Monday — two to expand background checks on gun sales and two to restrict suspected terrorists from buying guns.

Collins’s proposal  includes a five-year “lookback provision” to alert the FBI when someone who used to be on one of those lists purchases a firearm — in a nod to Omar Mateen, the Orlando shooter, who was on on a watch list before being removed by investigators.

To address concerns over due process for those mistakenly placed on a watch list, the proposal would allow U.S. citizens and green-card holders to file a legal appeal if they felt they were wrongly denied a firearm. The burden would then be on the government to prove its case and cover the person’s legal fees if they were found to be erroneously placed on a list of suspected terrorists.

That last provision has given some Republicans pause. The GOP argued passionately against Feinstein’s measure featuring a similar procedure to challenge cases where the government may have mistakenly listed someone as a suspected terrorist.

Republicans argue that measure didn’t sufficiently protect due process, and instead they rallied behind an alternative from Sen. John Cornyn (R-Tex.) that would have required the government to prove in three business days there was probable cause for someone to be on a watch list.

Collins said last week that the Cornyn proposal “doesn’t do the job” on closing the terrorist loophole.

And in the past week, she has earned support from a small group of Republicans, including pro-gun senators such as Lindsey Graham (R-S.C.), who all but dared his fellow GOP members and the National Rifle Association on Tuesday not to back Collins’s measure.

“If you vote against this, and [people on this list] do go out and [get] a gun and kill a bunch of people, you’ve got a lot of explaining to do,” Graham said, saying every constitutional right “has boundaries on it.”

NRA lobbying arm director Chris Cox called Collins’ proposal “unconstitutional” in a statement Tuesday, adding that it “would not have prevented the Orlando terrorist attack.”

Graham also called it an “inconvenience” at worst if someone on the list turns out to be mistakenly prevented from getting a gun right away, compared with the potentially catastrophic consequences if a terrorist bent on mass casualties manages to acquire a firearm.

“I own an AR-15 — if you’re on this list, it doesn’t bother me one bit that you can’t buy one right away,” Graham said. “Here’s the tiebreaker: We can fix the problem with an innocent person. Once the gun’s gone, we can’t fix that.”

Some Republicans appear inclined to consider the Collins compromise.

“It’s a step in the right direction. I’m not sure if it gets my vote, but we’re going to take a serious look at it,” Sen. Tim Scott (R-S.C.) said Tuesday.

“The key thing’s obviously the due process, is always the issue,” said Sen. James Lankford (R-Okla.). “If we can figure out a way to make that work, I’m glad to be able to do it.”

Others were more skeptical.

“This is one of those issues that’s pretty cut and dry where people are,” said Sen. Pat Roberts (R-Kan.). “People’s view on this haven’t changed much. It’s just the way it is.”

On Tuesday, Sen. Tim Kaine (D-Va.), also a member of Collins’s negotiating team, made the case that passing Collins’s proposal paves the way for more gun-control bills, such as an expansion of background checks.

“If this passes, it will give us more leverage to be able to fix it,” he said.

Kelsey Snell contributed to this report.