"Our law enforcement officials face a sea of illegal weapons flooding our streets, but the TRACE Act will close the loopholes that allow criminals to obtain illicit guns and choke off the supply to traffickers," he said.

Quigley's bill would repeal a number of measures passed in the last decade that were sponsored by former Rep. Todd Tiahrt (R-Kan.), often called the Tiahrt amendments. One of these, for example, requires data on gun background checks to be destroyed after 24 hours; Quigley's bill would require these records to be maintained for at least 180 days.

Quigley says such rapid destruction makes it almost impossible to catch gun purchasers who falsify their records or straw purchasers who buy guns for people who could not pass a background check.

The Tiahrt amendments also require all law enforcement data on firearms traces to be kept confidential, but Quigley's bill would strike down that requirement. Mark Glaze, director of Mayors Against Illegal Guns, said this change would go "a long way toward restoring access to critical gun data that can help protect our communities."

The National Rifle Association supports current law and says people want access to data on firearms traces in order to pursue lawsuits against firearm manufacturers. 

"NRA is committed to ensuring confidentiality of sensitive law enforcement information, and strongly opposes any effort to repeal the Tiahrt Amendment or any effort by the executive branch, or by state or local governments, to avoid its restrictions," the group wrote in a statement earlier this month.

Also under the bill, gun dealers would have to perform inventory checks and report lost and stolen guns. And it would require new firearms to be made with a second serial number located inside the weapon, where it would be more difficult to remove.

Quigley's bill is supported by Reps. Judy Chu (D-Calif.), Ted Deutch (D-Fla.), Raúl Grijalva (D-Ariz.), Barbara Lee (D-Calif.) and Jim MoranJames (Jim) Patrick MoranDems face close polls in must-win Virginia Billionaire Trump donor hires lobbyists to help vets Lawmakers: Chaffetz has a point on housing stipend MORE (D-Va.), and Del. Eleanor Holmes Norton (D-D.C.).