For the first time since the Sandy Hook massacre, the Senate Judiciary Committee approved a bill aimed at combating gun violence, one that may have the best shot at eventually becoming law. Washington D.C. bureau reporter Michael Scotto filed the following report.

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WASHINGTON -- A bill aimed at stopping gun trafficking made its way out of the Senate Judiciary Committee Thursday.

The legislation would make it easier to curb the flow of illegal guns across state lines and impose stiff prison sentences on so-called straw purchasers, people who buy firearms for those who are prohibited from doing so.

"This is a bipartisan bill that begins to crack down on one of the toughest problems we have with gun crime," said Sen. Kirsten Gillibrand of New York.

The bill is based, in part, on legislation introduced by Gillibrand.

The Judiciary Committee vote went mainly along partisan lines, but Iowa Republican Chuck Grassley supported it.

"I do think that action can be taken on gun trafficking and straw purchasing," Grassley said.

The Republicans who opposed it feared the bill might be too broad and lead to the arrest of innocent people. But they didn't close the door to supporting it down the road.

"I do think there is potential, before this bill is voted on in the floor of the Senate, to reach some bipartisan agreement that could end up having wide agreement," said Sen. Ted Cruz of Texas.

At the moment, the bill appears to be the only one that appears to have a shot at becoming law. Republicans remain strongly opposed to a ban on assault weapons, and negotiations over legislation that would require universal background checks have hit a snag.

Gillibrand said the trafficking bill might eventually lead to broader support for other legislation.

"I think this is a debate that the American people are ready to have, and I think if you can have one success, you can build it on for the next one," she said.

Mayor Michael Bloomberg is trying to drive that debate. His group, Mayors Against Illegal Guns, is out with a new ad.

In addition, polls taken from across the country show support for expanded background checks. But whether all of that translates to support in Congress remains uncertain.