Sen. Chris Murphy’s marathon 15-hour filibuster in early July captured the country’s attention, but it didn't resolve what Congress should do to prevent suspected terrorists from purchasing firearms.

Currently, federal law makes it illegal for gun shops to sell firearms to customers who fail to meet certain requirements — because they have a felony conviction or a certain mental health history, for instance.

But that test, a.k.a. a background check, doesn't currently block gun purchasers who are suspected of terrorism. As President Barack Obama has lamented, that means the FBI can't prevent a known terrorist from buying a weapon — even if federal authorities think an attack is possible.

In 2015, 244 people on the watch list of "known and suspected terrorists" tried to buy firearms. Of those, 223 were approved — a shocking 91 percent, as Sen. Chuck Schumer pointed out.

Especially in the wake of the Orlando mass shooting on Sunday, in which a shooter who had been under investigation by the FBI twice for incendiary comments killed 49 people, lawmakers want to stop that from happening.

They want to make a gun customer’s suspected involvement with terrorism — as determined by the US government — a reason to consider prohibiting him or her from buying a gun.

There’s a big fight right now in Congress over the right way to do that. Senators are currently debating three main proposals aimed at closing what Democrats call "the terror gap."

What the Democratic caucus wants: federal veto power over gun purchases by suspected terrorists

Sen. Dianne Feinstein’s proposal, backed by Murphy and the overwhelming majority of Democratic senators, would give the government broad authority to block gun sales to those who had been investigated in connection with terrorism.

It would do this by making two significant changes to the current system: one change that would put more people under additional scrutiny, and one that would give the government the power not just to scrutinize them but to block their gun purchase.

Under current law, the FBI is already notified whenever someone on a "known or suspected terrorist" list (drawn from existing terrorism databases) tries to purchase a gun. Under Feinstein’s legislation, they would also be notified of a gun purchase attempt by anyone who’s under investigation for terroristic activity — or who has been investigated anytime in the past five years.

Now, just because the name is flagged doesn't mean that the government would then automatically prevent that person from buying a gun, Ashley Schapitl, Feinstein's press secretary, says. "It merely refers them for additional scrutiny."

Once someone was flagged, the government would then have the power to veto gun purchases on terrorism grounds — a power it doesn't have right now. But to block the sale, the government would have to have reasonable suspicion that the person represented "a threat to public safety" and was considering or engaging in terrorist activities. (Here’s the exact wording from the amendment on what a "threat to public safety" would entail.)

That way, at least in theory, the government could block terrorists from getting weapons while also making sure it wasn’t blocking anyone who’d ever ended up on a terror watch list.

Republicans’ competing proposal: bring every gun-block case before a judge

Republicans and the National Rifle Association have objected that this proposal gives the federal government way too much power. If the government has the power to block anyone based on its own suspicions, what’s to stop it from abusing that power against law-abiding gun owners?

In response, Republican Sen. John Cornyn of Texas has drafted a bill that tries to close the "terrorist gun loophole" without also giving the federal government undefined amounts of authority.

Its central feature: To stop someone from buying a gun, the government has to prove in court that there’s "probable cause" the gun buyer will commit an act of terrorism, according to Sarah Trumble of Third Way. Under Cornyn’s proposal, the government would also only have 72 hours to file the paperwork to do so.

From one perspective, Cornyn’s proposal represents an effort to have the courts serve on a check on federal overreach. In theory, that would give the courts the ability to stop the executive branch from arbitrarily barring the everyman from buying a gun.

"If Democrats are actually serious about getting a solution on that issue, not just making a political talking point, they’ll join with us to support Senator Cornyn’s" bill," Republican Majority Leader Mitch McConnell told the Washington Post.

But most gun control experts and congressional experts view that proposal as a nonstarter, according to Trumble. There’s just no way that the federal government could be feasibly expected to marshal that kind of evidence — and to do so under such a high evidentiary standard within three days, she said.

"It’s just an absurd standard: It would not only be difficult to prove in court but our prosecutorial bodies just are not functional to that degree," Trumble said.

A third proposal emerges from Sen. Pat Toomey: a list approved by surveillance court

A third proposal has emerged recently through an effort spearheaded by Pennsylvania Sen. Pat Toomey, a Republican who is facing a very tough reelection bid.

Under Toomey’s proposal, like Feinstein's, the Department of Justice would have some authority to block gun sales to suspected terrorists. But rather than being able to do so unilaterally, Toomey’s proposal would create a different kind of judicial oversight over the executive branch's decisions.

In this scenario, the attorney general would have to submit a list of names to the secret Foreign Intelligence Surveillance Court for approval. The federal government could then only block gun sales to people on the FISA court-approved list. (The FISA court itself has been frequently criticized for its secrecy and lack of oversight.)

Toomey’s bill would also raise the bar the government would have to clear to block a gun sale. Unlike Feinstein’s bill, which allows the government to block a gun sale to anyone it suspects to be engaging in terrorism, Toomey’s proposal would only permit blocking sale to those officials believe will use a firearm in connection with terrorism, said Trumble.

Like most Democratic senators, Trumble argued that this proposal runs into a similar roadblock as Cornyn’s: It’s just not feasible.

"It’s probably impractical because the FISA court would have to verify every single person," Trumble said. "They just won’t be able to do that."

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