CHICAGO (CBS) – A day after a gun trafficking law named after slain Chicago teen Hadiya Pendleton made its way to the Senate floor, U.S. Sen. Dick Durbin (D-Ill.) said he believes it has the best chance of becoming law out of all the gun control proposals being considered on Capitol Hill.

WBBM Newsradio’s Mike Krauser reports Durbin co-sponsored the legislation introduced by U.S. Sen. Mark Kirk (R-Ill.), in an effort to crack down on so-called “straw purchasers,” who legally buy guns and then sell them to others who can’t. Current federal law does not explicitly ban straw purchasing.

Hadiya’s parents stood with Durbin and Police Supt. Garry McCarthy on Friday at Police Headquarters to talk about the effort.

Her mother, Cleopatra Cowley-Pendleton, said, “We need to allow other mothers to see their children to prom, and parenting, and everything else.”

She urged the Senate to move quickly to approve the straw purchasing ban and send the measure to the House for a vote there.

“I’d like to appeal to the Congress to actually give us a vote to make sure that this goes through. It just makes sense,” she said.

McCarthy said straw purchasing is probably the most common method for criminals to get guns.

Durbin said, right now, buying a gun for someone else is little more than a paperwork offense.

“For straw purchasers, for those who are going to buy guns and turn them over to the thugs and criminals: get ready. You’re going to deal with a hard-time federal crime,” he said. “Girlfriends, think twice. Is it worth 15 years in prison to buy that gun, and to go and sell it to some gang banger or some boyfriend?”

Durbin said he believes the straw purchasing ban is more politically viable than a federal ban on assault weapons or high-capacity ammunition clips, or a law mandating universal background checks.

The straw purchasing ban received bipartisan support in the Senate Judiciary Committee.