Universal background checks for gun purchases may be the most popular federal law that does not exist. Polls have shown that as much as 97 percent of the American public supports vetting every gun buyer for a history of high-risk behavior, regardless of whether they’re buying from a licensed firearms dealer, private seller, or internet posting. Large majorities of Republicans are in favor of the policy. Ditto gun owners and National Rifle Association members.

NRA leaders, however, have opposed federal legislation that would create universal background checks, and the organization’s allies in Congress have followed suit. That bloc used to include a handful of red-state Democrats. But with the political parties now almost perfectly aligned on opposite sides of the gun issue, the primary obstacle to universal checks is the Republican caucus. With the Democratic-held House passing a universal background check bill this February, the more specific obstacle is the GOP-led Senate. In the absence of universal background checks, an estimated 20 percent of gun sales have continued to go through without government screening for the purchaser.

Following the outbreak of mass shootings in Northern California, Brooklyn, Texas, and Ohio, pressure is mounting on Senate Majority Leader Mitch McConnell to allow a vote on gun reform legislation. Republican donors say a failure to act could mean their “extinction” with critical suburban voters. Strategists for the party see universal background checks as a potential opportunity for bipartisan consensus.

Congress is in recess until early September, and the winds may yet shift again. But as of August 6, here are the Republican senators expressing support for universal background checks as a response to this summer’s rash of shootings:

SENATORS

Patrick J. Toomey, Pennsylvania: “While no law will end mass shootings entirely, it’s time for Congress to act to help keep our communities safer,” he said in a statement on Sunday. “We should start by passing bipartisan proposals such as my legislation with Senator Joe Manchin to expand background checks to all commercial firearm sales,” a reference to a bipartisan bill blocked by pro-NRA senators in the wake of the Sandy Hook Elementary School massacre.

Lamar Alexander, Tennessee: Alexander is one of the three committee chairpersons McConnell has tapped to consider gun measures. “I am ready to do more, especially on background checks, to identify those who shouldn’t have guns,” he told The New York Times.

Mike Braun, Indiana: “Any bipartisan legislation to address gun violence must include stronger background checks and ‘red flag’ laws,” he told the Times.

Susan Collins, Maine: “I have long supported closing loopholes in background checks to prevent the sale of firearms to criminals and individuals with serious mental illness,” she tweeted on Sunday.

Rob Portman, Ohio: “Do we need more laws? Yeah, we probably do. And I think there’s a consensus now that we need background checks,” he said at a news conference on Sunday.