Mr. Coburn said the system, as proposed, presumed a “guilty until proven innocent” mentality that runs counter to American jurisprudence, pointing out the average time between a gun sale and a gun being used in a crime is 11 years.

“What we were going to do is put at risk gun owners who actually followed the law and 11 years later can’t find a piece of paper that said they did it right and the presumption is, you’re guilty,” he said. “And the vast majority of gun owners in this country and law-abiding citizens do not want to sell a gun to somebody that shouldn’t have it. And they’ll follow this.”

Mr. Coburn said that “some type” of enhanced background checks will pass the Senate.