"I would say that the likelihood is that they're not going to be able to get an assault weapons ban through this Congress," David Keene told Candy Crowley Sunday on CNN's "State of the Union."
On Sunday, Keene told Crowley he also didn't think limits on the sale of high capacity magazines could pass Congress either.
He said "the pieces are so cheap" it would be difficult to argue for regulation, Politico reported.
Echoing a statement released Friday, Keene said there was little progress in the NRA's meeting with Vice President Joe Biden, head of the White House task force on gun violence.
"We suspect that all he wanted to do was to say he talked to us, and now they're going to go forward and do the things they wanted to do," he was quoted by The Hill as saying.
Biden plans to deliver the task force's recommendations to President Barak Obama this week.