Sen. John McCain (R-Ariz.) expressed optimism Sunday that a measure to expand background checks on gun purchases could win support from most senators.

"There [are] some senators, bipartisan again, Sen. [Tom] Coburn (R-Okla.) and Sen. [Joe] Manchin (D-W.Va.) and some others who are working on package that I think that most of us will be able to support," McCain said on NBC News' "Meet The Press."

The group McCain referred to has been working to develop a proposal to expand background check requirements on gun purchases. Under current law, transactions involving licensed gun dealers require background checks, while others do not.

There is a growing consensus on Capitol Hill that a law requiring universal background checks stands a better chance of winning passage than a proposed ban on assault-style weapons.