“The public has supported the assault weapons ban, and they really support it when you remind them that we had it already and that these are weapons that the military uses,” said Celinda Lake, a Democratic pollster. “The intensity has always been on the anti-gun control side. Now the intensity is shifting onto the other side and the refrain out of Dayton — which is exactly the refrain the public has — is, ‘Do something.’”

The 1994 law, which passed as part of a broader crime bill championed by Mr. Biden, then a senator, banned the sale of 19 specific weapons that have the features of guns used by the military, including semiautomatic rifles and certain types of shotguns and handguns. It also outlawed magazines that can hold more than 10 rounds of ammunition. But people who already had such weapons were allowed to keep them.

For years, the ban was considered politically toxic for Democrats. After Mr. Clinton signed it into law, Democrats were trounced in the midterm elections. They lost control of the House, which they had held for 40 years. Among the losers was Tom Foley, who drew the ire of the National Rifle Association when he came out in favor of the ban and was the first sitting House speaker to lose an election since 1862.

The outcome rattled Democrats, and their fears of the N.R.A. only grew after Al Gore lost the presidential election to George W. Bush in 2000. Many Democrats, including Mr. Clinton, blamed the loss on Mr. Gore’s stance on gun control. Four years later, the assault weapons ban expired.

Now the politics are shifting. The N.R.A. is weakened, bogged down by outside investigations into alleged financial wrongdoing. Democrats are far less likely to rely on rural voters than they were two decades ago. And support for gun control is strong in cities and suburbs, especially among women in suburban districts like the one Mr. Crow represents.

The NPR poll found that 89 percent of Americans supported background checks on all gun purchases, including those at gun shows and online. And since the shootings in El Paso and Dayton, Democrats and Republicans have embraced so-called red flag laws, which make it easier for the authorities to take guns from those deemed dangerous by a judge.

The assault weapons ban, though, remains contentious. The N.R.A. and Republicans have vigorously opposed it, arguing that it is ineffective and infringes on the Second Amendment. Its backers know it will never pass the Republican Senate and instead are making the case for what Democrats would do if they were in charge.