Mourners enter the Sutherland Springs First Baptist Church in Sutherland Springs, Tex., to view a memorial. A man opened fire inside the church in the small South Texas community, killing more than two dozen people last month. (Eric Gay/AP)

Rare bipartisan consensus around legislation to improve the national background check system for gun purchases is in jeopardy after House Republicans linked the measure to a bill allowing gun owners to carry concealed weapons across state lines.

The House is expected to vote and pass the combination bill Wednesday over the objections of House Democrats, who accused Republicans of “trickery” and “sabotage” in tying the background checks bill to a concealed-carry measure the National Rifle Association called its “highest legislative priority.”

In the Senate, Democrats have labeled the concealed-carry legislation a nonstarter, while leading Senate Republicans cautioned that pairing the bills is a recipe for the demise of both.

“When you put them together, it makes it harder for us to do what we can do, and can do now,” said Sen. John Cornyn (R-Tex.), the Senate’s No. 2 Republican and a co-author of the background checks legislation. “I want to separate those two out, get the “fix NICS” bill passed, and hopefully save some lives.”

The background-checks legislation, which forces federal agencies and encourages states to better report offenses that prohibit individuals from buying firearms, is the first gun bill in years to secure the support of Democrats, Republicans, gun-control advocates and the NRA. Bill authors credit its narrow focus — shoring up the National Instant Criminal Background Check System, known as NICS — for keeping together an otherwise unwieldy coalition of support. They caution against upsetting the balance by loading up the bill with other measures.

“When we were negotiating in a very bipartisan, good-faith way, the understanding was the NICS-fix bill would be considered on its own,” said Sen. Richard Blumenthal (D-Conn.), an original co-sponsor of the bill. “Combining them would be completely unwise and unacceptable, and everyone knows it.”

But supporters of the House GOP effort argue that the concealed-carry legislation is a logical complement to the background checks bill.

“Taken together, these two bills preserve and protect the rights guaranteed to us by the Second Amendment,” House Judiciary Committee chairman Bob Goodlatte (R-Va.) said Tuesday. “I believe that both bills complement each other in keeping people safe.”

Lawmakers began drafting legislation last month to improve reporting to the background check system after it emerged that the shooter in a deadly attack on a church in Sutherland Springs, Tex., could have been prevented from buying guns if the military had reported a domestic violence charge to the NICS database. The background checks effort has been more successful than a Democratic-led push to respond to the October mass shooting in Las Vegas, with a ban on “bump stocks” — an add-on that turns a semiautomatic weapon into an illegal, automatic one.

The bump-stocks matter is largely on hold in Congress, as GOP lawmakers, under NRA pressure, defer to a new Justice Department effort launched Tuesday to “clarify whether certain bump stock devices fall within that definition” of “machine gun,” a prohibited category of firearm. The Senate Judiciary Committee is nonetheless expected to discuss bump stocks at a hearing Wednesday that is also slated as the official start to the Senate’s debate about improving NICS reporting.

Gun-control advocates urging the Senate process along are at the same time excoriating House Republicans for what they see as complicating the debate.

“Instead of doing what’s right, Congress is attempting to do what the gun lobby wants them to do, which is to pass this concealed-carry reciprocity law,” said Mark Kelly, who co-founded the gun control group Giffords with his wife, former Democratic congresswoman Gabrielle Giffords, who left the House after becoming a victim of gun violence in her home state of Arizona.

Kelly said that he and Giffords are “both offended and outraged that Republicans are trying to tie this bad piece of legislation to something that’s trying to do something positive.”

Giffords and the liberal-leaning litigation and policy organization Democracy Forward filed a lawsuit Monday against the Justice Department, alleging that the department has failed to turn over documents showing how the gun lobby is attempting to influence federal firearms policy, including by pushing concealed-carry reciprocity after the Las Vegas shooting. The Justice Department declined to comment on the lawsuit.

Lawrence G. Keane, senior vice president and general counsel for the National Shooting Sports Foundation, said the decision of how to package these bills has always been up to lawmakers.

“We support both bills, and if they get combined we’ll support the combined bill — and if they’re not combined we’ll support both bills separately,” Keane said. “They’re both good bills and they both should pass, and Americans should be allowed to exercise their constitutional right.”

NRA spokeswoman Jennifer Baker applauded the House for being “on the eve of voting for the biggest expansion of self-defense rights in modern American history.”

But some Democrats in the Senate are shrugging off the House’s maneuver as an empty threat — both because of Cornyn’s resistance and because by their count, only a handful of Senate Democrats might possibly vote for concealed-carry legislation. It would take the support of eight Democrats, in addition to every Senate Republican, to clear the 60-vote procedural hurdles a gun bill would face.

“I don’t think it changes anybody’s vote,” said Sen. Chris Murphy (D-Conn.), a lead author of the background checks bill. “I don’t think the votes are there in the Senate to pass concealed carry.”