Mr. Rosendale entered the Republican primary race less than a week ago, but Donald J. Trump’s quick endorsement of his main rival left him facing an uphill fight.
President Biden and Transportation Secretary Pete Buttigieg made public calls for Republicans, who remain at an impasse over funding the government, to resolve their differences before next Sunday.
The defectors broke with their party to block a Pentagon spending bill from being debated in the House. Their stances reflect deep G.O.P. divisions pushing the government toward a shutdown.
Members of the ultraconservative Freedom Caucus effectively shut down the House floor for several hours, calling the speaker’s fiscal compromise with President Biden a betrayal.
The rebellion has been led by a small but vocal group of ultraconservative Republicans. But there are other, less-known defectors who could help scuttle the G.O.P. leader’s candidacy.