Running a third-party candidate against Donald Trump in the general election, as some Republicans are looking to do, would be a "suicide mission," Republican National Committee chairman Reince Priebus said Sunday.

"This is a suicide mission, it is not right," Priebus said in an interview with CBS' "Face the Nation." "And I think what people should do is take the Paul Ryan approach which is to work with Donald Trump and find out whether or not there's common ground ... as opposed to blowing everything up."

Priebus was referring to a Washington Post report from this weekend saying a group of Republicans frustrated with Trump, including 2012 GOP nominee Mitt Romney, are actively working to recruit a candidate for an independent presidential bid. The group's top prospects, reportedly, are Nebraska Sen. Ben Sasse and Ohio Gov. John Kasich.

The RNC chief argued that a third-party run would virtually guarantee a Clinton victory in November--and that that would mean not just another Democratic president in the White House, but potentially a far more liberal Supreme Court in the coming years.

As for the stories about Trump posing as his own spokesman, "John Miller," to promote himself, Priebus said it's "odd" but suggested voters won't care about things like that.

"It's a little bit odd, but I will just tell you that I think of all the things facing this country right now and being through this primary for a year, I can assure you that particular issue is not going to move the electorate," he said.

Priebus said voters will be more focused on the difference between Democrat Hillary Clinton "and a guy who's never run for public office, a business guy who's a total outsider that's going to cause an earthquake in Washington."

"There's going to be lots of stories," he added. "My guess is it's not going to move the electorate."

Priebus had the same answer about Trump's taxes, which the GOP candidate has said he is unlikely to release until after the election. (Trump has since worked to clarify his comments, saying he'll release his taxes when he is no longer being audited.) Despite the fact that he'd be the first major party presidential nominee since 1976 to refrain from releasing his taxes, Priebus said it wouldn't hurt him politically.

"I wouldn't be surprised if people don't care," he said. "...Donald Trump has rewritten the traditional playbook in politics, and I don't know if anyone else could have pulled off what he's pulled off over the past year."

"People are angry, people want something done right this second and Donald Trump has effectively represented that position," he added.

Priebus also spoke about Trump's meeting with House Speaker Paul Ryan last week, saying that though the two men disagree on some issues they have far more common ground than differences.

"I think they agree on far more than they disagree on," he said. "Look, I think you've got about 80 percent overlap and you've seen actually Donald Trump this week nuance a little bit on some of those positions that you've just outlined. So I think we're gonna get there."