The Arizona Republican pointed to a plan being drafted by Sens. Tom Coburn (R-Okla.), Chuck Schumer (D-N.Y.), Mark Kirk (R-Ill.) and Joe Manchin (D-W.Va.) that is expected to focus chiefly on overhauling background checks to ensure all prospective owners’ histories are vetted. That proposal is expected to be unveiled in the coming days.

“I think most of us will be able to support” that plan, McCain said on NBC’s “Meet the Press.”