Congress should not vote during the lame-duck session on whether to repeal the "Don't ask, don't tell" ban on gay people serving openly in the military, Sen. John McCainJohn Sidney McCainGOP senators appalled by 'ridiculous' House infighting MSNBC's Nicolle Wallace, Chris Christie battle over Fox News Trump's attacks on McConnell seen as prelude to 2024 White House bid MORE (R-Ariz.) said on "Meet the Press" on Sunday.

McCain said that he expects a major report to be issued in early December on the impact of a repeal.

After that, members of Congress should have time to review the report and hold hearings on the study and its findings. 

"Once we get this study we need to have hearings and we need to examine it and…and see if it's the kind of study we wanted," McCain said.

He reiterated his view that the study must examine "the effect [of a repeal] on morale and battle effectiveness on the U.S. Army" rather than what policy is most popular, he said.

McCain also addressed an appearance by his wife Cindy McCain in a commercial that seemed to critique the "Don't Ask, Don't Tell" policy. She has since said she supports her husband's view on the issue.

McCain laughed when the issue came up.

"I respect the First Amendment rights of every member of my family," he said.

Sen. John CornynJohn CornynMental health: The power of connecting requires the power of investing Senators call for Smithsonian Latino, women's museums to be built on National Mall Cornyn says he 'would be surprised' if GOP tries to unseat Sinema in 2024 MORE (R-Texas) said on CNN's "State of the Union" that he didn't think there would even be time to address "Don't ask, don't tell" in the lame-duck session because the continuing resolution to keep the government operating and the extension of the Bush-era tax cuts were more pressing.

"I don't think there's a lot of time," Cornyn said. "And I don't think there's a lot of appetite to try to jam stuff through."