A right-wing congressman will run for Senate in Montana, fueling a battle against the GOP

Mr. Rosendale and Mr. Gaetz were part of a small group of Republicans who ousted Rep. Kevin McCarthy as Speaker of the House, temporarily shutting down business in the chamber. Mr. Rosendale objected to the appointment of Mr. McCarthy in the role, he appeared to dismiss a phone call to the House from Mr. Trump, who called Ms. Greene to ask for his support.

Mr. Rosendale also has the support of Stephen K. Bannon, a former Trump White House strategist who is planning a campaign blitz in Montana next month. Mr. Rosendale was a frequent guest on Mr. Bannon’s “War Room” podcast, which is popular among conservatives.

Mr. Rosendale entered 2024 with $1.7 million in his federal campaign account. That is about 40 percent of what he spent against Mr. Tester six years ago, but a small fraction of the money expected to go into efforts to nominate Mr. Sheehy, a retired Navy SEAL who founded an aerial firefighting company.

Two super PACs linked to traditional Republicans — the Senate Leadership Fund, which has ties to Sen. Mitch McConnell, the Republican leader, and American Crossroads, which was co-founded by Karl Rove — have each earmarked about $22 million for advertising in the state for the general election.

A third super PAC supporting Mr. Sheehy, known as More Jobs, Less Government, is underwritten by several wealthy Wall Street executives. Kenneth Griffin gave $5 million, Paul Singer $1 million and Stephen A. Schwarzman contributed $400,000, according to Federal Election Commission data. The super PAC has hired Tony Fabrizio, Mr. Trump’s longtime pollster, and Andy Surabian, a strategist who has been involved in all three of Mr. Trump’s presidential campaigns.

Mr. Tester, meanwhile, kept up with the rise in Republican spending. His campaign spent $5 million on advertising in the state, aided by two Democratic super PACs, WinSenate and Last Best Place Last. Together, they spent about $50 million, most of which was general election ad bookings. The two PACs have ties to Senate Majority PAC, the top Democratic caucus in the Senate.

Maggie Haberman contributed to the reporting.

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