Gun control advocates were on Capitol Hill Tuesday afternoon to ask members of Congress to pass legislation that would tighten gun-buying restrictions. It was part of the Mayors Against Illegal Guns campaign, led by New York Mayor Michael Bloomberg and Boston Mayor Tom Menino, to make it more difficult for convicted criminals and people found mentally ill from purchasing guns.

Menino and Bloomberg claim that gaps in recordkeeping by local, state and federal government agencies across the country keep important criminal and mental health information out of the background checks firearm sellers are required to make before making a sale. They're calling on Congress to pass a bill, sponsored by Sen. Charles Schumer (D-N.Y.), that would require state and local agencies to share such information with the National Instant Criminal Background Check System, a gun-buying background check system administered by the FBI.

The bill, also known as the Fix Gun Checks Act of 2011, was the subject of a Senate Judiciary Crime and Terrorism Subcommittee hearing attended by law enforcement officials, advocates on both sides of the issue, and a few survivors of the Tucson shooting in January that left six dead and seriously wounded Ariz. Rep. Gabrielle Giffords. Bloomberg, who was scheduled to testify, was unable to make it; he was represented by Chief Advisor John Feinblatt.

"The tragic fact is, background checks often don't happen," Feinblatt said during his testimony. "If they do, they don't have all the information they should."

The most controversial part of Schumer's legislation would also tighten gun-buying restrictions for the mentally ill. Current law bars those who have been "adjudicated as mentally ill" from owning firearms, but the language is so vague that many states do not enforce it.

Schumer's bill defines "adjudicated as mentally ill" as those who have been ordered to mental counseling by a "court, commission, or other lawful authority." David Kopel, a constitutional scholar at the University of Denver who testified at Tuesday's hearing, said that language could produce a lot of unintended consequences. For example, victims of rape on a college campus could be ordered by the administration to receive counseling, as could police officers involved in shootings while on duty, he said. The law could be interpreted to bar them from buying firearms.

The bill would also strengthen current laws barring drug addicts from buying guns - it would bar anyone ordered to drug treatment or counseling by a court, regardless of whether they were found guilty or convicted, from purchasing a firearm. Kopel called it an "overreach" of legislative powers, which Schumer shrugged off.

"[People] can't be ordered to counseling willy-nilly," Schumer said. "You can't be ordered into counseling very easily."

After the hearing, Mayor Menino joined Schumer, Democratic Rep. Carolyn McCarthy of New York (who sponsored a similar bill to Schumer's in the House), and gun control advocates for a press conference outside the hearing room. McCarthy talked about a related bill she's sponsoring in the House, which would require background checks for people purchasing weapons at gun shows.