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The Lugar campaign knew it was in trouble last week when a final poll showed him trailing Mr. Mourdock by a full 10 points, more than undoing the slim lead he had held for the past few months.

Meanwhile, Mr. Mourdock, 60, solidified his status as a tea party darling in recent weeks, pocketing endorsements from former Sen. Rick Santorum of Pennsylvania, Rep. Michele Bachmann of Minnesota and former Alaska Gov. Sarah Palin and sticking to his core message that Mr. Lugar had been in Washington too long.

“Honestly, as I look at our nation’s capital, I feel more frustrated with Republicans than Democrats,” he told voters at a Lincoln Day dinner on Sunday. But “bipartisanship has taken us to the brink of bankruptcy. It is not bipartisanship we need; it is principle.”

Other tea party-backed candidates are striving to overthrow establishment Republicans in Texas and in Utah, where former state Sen. Dan Liljenquist forced Mr. Hatch into a primary in June. In 2010 in Utah, three-term Republican Sen. Robert F. Bennett was defeated by a GOP challenger, Mike Lee, who went onto hold the seat for the GOP.

Mr. Lugar hadn’t faced a primary challenger since joining the Senate in 1976, and it showed. He appeared rusty on the campaign trail as he struggled to convince voters that his experience with foreign policy and his ability to work across the aisle were strengths, not weaknesses.

Some analysts said he failed to take Mr. Mourdock seriously soon enough after the Tea Party Express announced last year that it would heavily back the second-term treasurer, giving him an strong initial boost.

Others said he could have done a better job of explaining issues before Mr. Mourdock had a chance to exploit them — such as a question of whether Mr. Lugar could even vote in Indiana, which was eventually resolved when election officials agreed he could register using the address of a family farm.

“It would have been better to just swallow hard on some things, whether it was residency or defending the votes for [Sonia] Sotomayor and [Elena] Kagan,” said Ed Feigenbaum, editor of several political newsletters in the state, referring to President Obama’s Supreme Court nominees. “And explaining, ‘Yeah, maybe it would have looked better if I had had a residency in the state, but I do have the family farm, no big deal.’ “

Mr. Lugar did tout his coveted endorsement from popular Gov. Mitch Daniels, a fellow Republican, airing several television ads with the governor praising his experience and reputation as a statesman. But even Mr. Daniels refused to denounce Mr. Mourdock, calling him a “thoroughly credible person who is a friend and ally of mine” last week.

The GOP presidential candidates were also on the ballot for Indiana voters, with 64 percent voting for Mitt Romney and 15 percent backing Ron Paul at press time.