But after hearing heated, emotional testimony, the measure's supporters and opponents seem no closer to agreement on any of the core issues. And given the gridlock in Congress, supporters of new gun legislation may not get everything they want - and might not get anything at all.
Since the first assault weapons ban became law in 1994, most Republicans, as well as many Democrats, have steered clear of the issue.
A series of recent mass shootings, however, emboldened supporters of gun restrictions to renew their push. For them, the last straw may have been the December shootings at Sandy Hook Elementary School in Newtown, Conn., in which a gunman armed with an assault rifle killed 20 children and six adults.
"We are holding today's hearing because the massacre in Newtown was, sadly, not an anomaly," said Sen. Dianne Feinstein, D-Calif., the lead sponsor of the new bill, as she opening Wednesday's hearing before the Senate Judiciary Committee.
One key witness was Neil Heslin, whose son, Jesse, was among the young Newtown victims. Weeping, Heslin said no family should have to endure what he and the other victims' families have had to go through.
All 21 current co-sponsors of Feinstein's legislation are Democrats, and while some Republicans said they were willing to have a vote on the bill, they've made it clear that they oppose it. Sen. Lindsey Graham, R-S.C., expressed a view shared by the National Rifle Association and many fellow Republicans that existing laws aren't sufficiently enforced.
"I'm a bit frustrated that we'd say one thing, but in the real world we do nothing to enforce laws on the books," he said.
Tempers flared when Graham asked Milwaukee Police Chief Edward Flynn whether police were arresting people who'd failed background checks to buy guns.
"We don't chase paper, we chase armed criminals!" Flynn thundered, generating applause from some members of the audience and a reprimand from Feinstein.
"Sen. Graham and I just got recognized for civility," she said, noting an award that both had received Tuesday. "Let's keep this civil."
Opponents have criticized Feinstein's proposals as feel-good measures that would do little to stop mass shootings but would hurt law-abiding gun owners. During the hearing, the NRA flooded Twitter with responses to the testimony, using the hashtag StopFeinstein to respond to every point.
Vice President Joe Biden on Wednesday asked a gathering of state attorneys general in Washington for their help in getting the measures through Congress.
"There will be a moral price, as well as a political price, to be paid for inaction," he said.
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