Cantor: Republicans won't shut down the government

Former House Majority Leader Eric Cantor said Monday the stunning resignation by House Speaker John Boehner could help avert a potential government shutdown.

"With John Boehner doing what he did, it creates the opportunity for the Republican members to come together—and a lot of them are calling for sort of a family meeting—and really discuss what is actually doable in a divided government," Cantor told CNBC's "Squawk Box."

"The Republican members have been there, done that on the shutdown question," he said. "I don't think you're going to see a shutdown."

About two dozen Republican Congress members have said they will not vote for any spending bill that funds Planned Parenthood. Lawmakers face a Wednesday deadline to fund the government.

Boehner, under fire from conservatives over the looming government shutdown, said Friday he will resign from Congress at the end of October. "Prolonged leadership turmoil would do irreparable damage to the institution," he said.

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Washington insiders told CNBC on Friday that Boehner had come under pressure from the GOP's tea party movement and conservative Freedom Caucus. They said his likely successor, Rep. Kevin McCarthy of California would probably have to strike a bargain with those groups.

Cantor, vice chairman and managing director at investment bank Moelis and Co., lost his 2014 GOP primary race to David Brat, a tea party-affiliated economics professor. Boehner, who was elected in 1990, said he had planned to serve only through the end of 2014 but he stayed on because of Cantor's defeat.

Cantor called the tea party and Freedom Caucus a "small minority" that has the ability to block legislation, but cannot actually accomplish anything. He said Republicans must set realistic expectations in a divided government.

"We have now been put in the position where all eyes are on us. Let's start to be honest with people about what we can get accomplished," he said.

Senate Finance Committee member Mark Warner, D-Va., said Monday Boehner's resignation would help lawmakers get through Wednesday's deadline, but ultimately, it only buys Congress 75 days before it faces another showdown over the budget and the country's debt ceiling. He noted that Boehner had been one of the Republicans willing to explore a grand budget bargain.

"I do think there are a lot more folks in both parties who are willing to do the right thing, but the extremes on both sides sometimes come in and chop your legs off," he told "Squawk Box."

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The fringe has come to dominate the Republican Party, he said. Across the aisle, some Democrats also have moved toward extremes, seeing how successful the absolutist position has been in the GOP, he added.

"In many ways, what I think has driven the rise of some of these nontraditional candidates on the right have been the failure of actually getting things done, and the only way that's going to happen is if we can find some common ground," Warner said.

Asked whether Republican presidential contender Jeb Bush would face pressure from the GOP's minority factions, Cantor acknowledged that conservatives are frustrated but said the former Florida governor has the vision to raise the standard of living for Americans and the ability to execute that vision.

Polls that show Washington outsiders Donald Trump, Ben Carson, and Carly Fiorina leading the Republican pack are "interesting and entertaining," but history has shown early polling is not reliable, he said.

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—CNBC's Everett Rosenfeld, Reem Nasr, and Matthew Belvedere contributed to this story.