House Republicans plan to vote this week on a bipartisan proposal to tighten up the federal background-check system following the massacre last month of 25 Texas churchgoers by a man whose history of domestic violence should have stopped him from buying a gun.

That vote would represent a breakthrough for advocates of gun control after years of congressional inaction in the wake of mass shootings—except for one enormous catch: Republicans are attaching the bipartisan bill to a separate measure that dramatically expands gun rights across the country. The second proposal, known as the Concealed Carry Reciprocity Act, is a top priority of the National Rifle Association; it makes permits to carry a concealed weapon issued in one state valid in most other states as well. The bill would also allow people to carry concealed weapons into national parks and other federally-owned lands.

Many states have strong background-check requirements or force applicants to undergo hours of gun-safety training before getting a concealed-carry permit. But many other states have weaker standards, and 12 states allow residents to carry handguns with no permit at all.

“This will force states with strong laws to honor the requirements of the states with the weakest, and it’s really just not right,” Mark Kelly told reporters on a conference call. He’s the retired astronaut and husband of former Representative Gabrielle Giffords of Arizona, who was shot at a constituent event in 2011.

Democrats accused Republicans of using the modest bipartisan reform of the National Instant Criminal Background Check System, or NICS, as a legislative sweetener to win votes for a much more radical loosening of gun laws. The so-called Fix NICS Act adds a combination of incentives and penalties to ensure that state and federal agencies submit records to the background-check database. After last month’s church massacre in Sutherland Springs, Texas, the Air Force acknowledged that it failed to enter the shooter’s court martial for domestic violence into the NICS database, which could have prevented him from buying the rifle he used in the killing spree.

“What we do in response to that horrific mass shooting should not be held hostage to the gun lobby’s No. 1 priority,” Kelly said. The Fix NICS Act also requires the Department of Alcohol, Tobacco, Firearms, and Explosives to report to Congress data on the use of bump stocks in gun crimes. That was the device used by the shooter who killed 58 people and injured hundreds more at a Las Vegas country-music concert in October. Democrats and some Republicans have called for an outright ban on bump stocks, which enable a gun to fire bullets at a much higher frequency, but the legislation does not go that far.

The chief sponsor of the concealed-carry legislation is Representative Richard Hudson, a Republican from North Carolina. In an interview on Monday, he told me it was not his decision to combine the two gun proposals into a single bill. He defended the reciprocity act as one that would force states to treat gun permits the same way as driver’s or marriage licenses. Hudson pointed out that while states would have to recognize permits issued by another, gun owners would still have to abide by each individual state’s laws on when and where they can carry a loaded weapon. He cited the example of Shaneen Allen, a single mother with a concealed-carry permit issued by Pennsylvania. In 2013, she spent 50 days in jail in New Jersey, which doesn’t have a reciprocity law, after she alerted police to her gun during a traffic stop. (Governor Chris Christie pardoned her.)

“You’re not going to see mobs of people carrying concealed [weapons] into Times Square,” Hudson told me. “But,” he continued, “law-abiding citizens who may be passing through one state to get to grandma’s house in the next state aren’t automatically going to become a criminal.”

A number of law-enforcement groups have come out against the bill, saying it would add to dangers faced by police officers on the beat. “This isn’t the Wild West,” said Kevin Davis, the Baltimore police commissioner. “The reality of it all is that police officers in Baltimore and elsewhere may be completely unable to confirm whether a person is indeed carrying legally.”

A spokesman for House Minority Leader Nancy Pelosi said an “overwhelming majority” of Democrats are expected to oppose the combined concealed-carry and background-check bill. Republicans might still be able to pass it on their own, but the bigger question will be the measure’s fate in the Senate, where at least eight Democratic votes would be needed to overcome a filibuster. Hudson’s office noted that seven Democrats currently serving in the Senate voted for a different concealed-carry reciprocity bill that was offered as an amendment in 2013.

But Senator Chris Murphy of Connecticut, the lead Democratic sponsor of the bipartisan Fix NICS bill, said he was confident that the GOP’s gambit wouldn’t work. “My impression is that if they combine the two, the bill is dead in the Senate,” Murphy told me. “So this is just theater this week in the House. This isn’t lawmaking.” Senator John Cornyn, the second-ranking Republican, told reporters last week that while he supported both bills, he didn’t think they should be combined. “Combining them, I think, is to risk doing nothing,” he said, according to the Daily Caller.

Murphy did see a bit of a silver lining for advocates of stricter gun laws, however. “It is interesting to me that Republicans in the House decided they couldn’t move the concealed-carry reciprocity by itself and that for PR reasons they felt they had to dress it up with the Fix NICS Act,” he said. “That tells you that there’s a political exposure for Republicans on the NRA agenda that simply was not there 10 years ago.” By combining the bills, Republicans are trying to entice Democrats to support them, or risk looking overly political by opposing efforts to improve the background-check system that they’ve vocally backed.

“It’s a pretty clumsy, transparent effort at trying to look reasonable,” Murphy said of the Republican maneuver. But that itself was a shift. In the past, he continued, “Republicans didn’t try to look reasonable.”