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Another re-election challenge was some voters’ lingering resentment to Mrs. Murkowski’s appointment to the Senate in 2002 by her father, who had vacated the seat to become governor, experts say.

Mrs. Murkowski, who had been significantly ahead in the polls this year, was accused by some of not taking her challenger seriously enough.

“He was a credible opponent from the minute he filed, and if you want to stay in office, if you want to survive, then you have to take that extremely seriously,” Mr. McBeath said. “That’s the only thing you think about doing. She didn’t.”

Mrs. Murkowski wasn’t the only Republican establishment candidate to struggle in Tuesday’s primaries nationwide, as multimillionaire health care executive Rick Scott edged Florida Attorney General Bill McCollum to win the state’s GOP gubernatorial primary.

Mr. Scott used a campaign tactic employed successfully by other outsider, tea party-backed candidates fighting establishment Republicans this year in intraparty contests; accuse your opponent of being a party insider who has abandoned true conservative values.

“You have the opportunity to vote for a principled, conservative outsider with a track record of creating jobs or a flip-flopping career politician,” said Mr. Scott in an e-mail to supporters earlier this month.

The Florida GOP, which strongly had backed Mr. McCollum, on Wednesday appeared to offer an olive branch to Mr. Scott.

“Republicans know what is at stake and will rally in support of Rick Scott as the campaign for governor moves forward,” said Florida Republican Party National Committeeman Paul Senft. “He has good, new and fresh ideas that will help the state of Florida during these difficult budget times.”

Republican Sen. Robert F. Bennett of Utah also was shown the door by party voters in April by denying him a spot on the party’s primary ballot.

Mr. Bennett, like many other incumbents, faced a general anti-Washington backlash. His support of the Wall Street bailout in 2008 further disenfranchised him from many party faithful.

Republican Reps. Parker Griffith of Alabama and Bob Inglis of South Carolina also have failed in their primary bids this year.

This story is based in part on wire service reports.