WASHINGTON — Remember bump stocks?

The previously obscure gun conversion kits, which turn semiautomatic rifles into weapons capable of firing long, deadly bursts, were the bane of the Capitol a month ago, after a gunman used the devices to kill 58 people and wound hundreds of others in Las Vegas. Lawmakers in both parties quickly vowed to ban them. Even the National Rifle Association appeared to endorse restrictions.

But the proposed ban on bump stocks, once hailed as a modest step toward bipartisan compromise on gun safety, may be turning into a cautionary tale of how energetic intentions in the wake of mass shootings can dissipate quickly. As attentions moved elsewhere, the N.R.A. turned against action, and Republican lawmakers decided the devices would be someone else’s problem: the Bureau of Alcohol, Tobacco, Firearms and Explosives, or A.T.F.

“Right now everyone’s in a holding pattern, because some people around here have hope that A.T.F. will bail us out,” said Representative Carlos Curbelo, Republican of Florida, who has co-sponsored a bipartisan measure to ban bump stocks.

And now, with another mass shooting, this one in Texas, capturing the nation’s lamentations, Congress is moving on to yet another gun issue, the failure of the government’s computerized background check system to stop firearms purchases by killers who should have been flagged. On Tuesday, Senators Jeff Flake, Republican of Arizona, and Martin Heinrich, Democrat of New Mexico, said they would introduce legislation to bolster the reporting of domestic violence acts to the background check system.