While its chances appear remote, based on the chamber's GOP majority, Obama and Democrats urged people to insist that their elected leaders pass the background check measure that has strong public support.
"You need to let your representatives in Congress know that you are disappointed, and if they don't act this time, you will remember come election time," Obama said.
Republican opponents of the new gun laws parroted the NRA position that expanding background checks would be a step toward a national gun registry and eventual federal confiscation of firearms, a claim that Obama and sponsors of the compromise called false.
Some opponents argued the language of the compromise would burden law-abiding gun owners seeking to sell their guns privately over the Internet.
Cornyn and others called for a more limited bill that would focus on keeping guns out of the hands of criminals and people adjudicated as mentally ill, rather than seeking to expand background checks beyond current limits.
Democrats responded that such an argument was contradictory, because the expanded background checks would prevent criminals and the mentally ill from obtaining firearms.
"It's inconceivable to me that someone could believe that you can keep guns away from criminals and the dangerously mentally ill without at a minimum having a background check," said Rep. Mike Thompson of California, who was leading the Democratic gun law effort in the House.
The debate over gun laws is not going away, according to West, the Brookings analyst.
"I expect this issue to remain on the public agenda," he said, "because shootings happen all the time and large numbers still favor tougher background checks."