LEXINGTON, Ky. — For Matt Bevin, the main challenger in the Republican primary to topple Senator Mitch Mcconnell of Kentucky, the campaign could be boiled down to this, his one chance to try to confront his opponent in person, in the crowded ballroom of a Marriott hotel.

He pushed, shoved and maneuvered close to the senator at a political dinner, only to be elbowed out of the way by Mr. McConnell’s wife, the former labor secretary Elaine L. Chao, and a couple of dexterous campaign aides.

“Pathetic,” Mr. Bevin grumbled.

That may also be a word to describe his once-promising, Tea Party-inspired campaign to unseat one of the most powerful figures in the capital, a man who first won election to the Senate in 1984 and whom Mr. Bevin has tried to portray as an out-of-touch creature of Washington.

Instead, Mr. Bevin, 47, has been forced to defend himself for showing up at a cockfighting rally; for padding his résumé; and for backing the bailout of big banks when he worked as an investment adviser, then calling the rescue “irresponsible” as a candidate.

Mr. McConnell, 72, is running such a confident race that during the recent two-week congressional recess, the dinner here was his only formal campaign event in his home state.

Tea Party groups that have bedeviled the Republican establishment for the past two election cycles — and helped upend Republican ambitions to seize Senate control — had high hopes for Mr. Bevin. And they had set their sights on the would-be Senate majority leader, whom they have seen as the consummate Washington deal maker, if not a liberal than a liberal enabler. But in many respects, Mr. McConnell seems to be thriving almost in spite of himself, yet another sign that at least for now, the Establishment has struck back.

“That’s all right. I was never under any delusion this was going to be easy,” Mr. Bevin said glumly in the hotel parking lot outside the Fayette County Republicans’ Reagan Day Dinner.

It was not supposed to be this way. Mr. Bevin had the backing of prominent Tea Party groups, with the promise of financial and grass-roots support, and it was believed that he would be able to capitalize on the senator’s low job approval numbers and a general anti-Washington mood.

“If you’re the leader, you have a tougher race,” Mr. McConnell, the minority leader, said in his trademark, affectless monotone. “You become a national target. We knew that coming in. We knew it’d be a war.”

Mr. McConnell has suffered few wounds so far in the conflict. But if he has benefited from the weakness of his opposition, that is likely to change after the May 20 primary, when he would face the Democratic candidate, Alison Lundergan Grimes, Kentucky’s secretary of state. Polls have consistently shown Ms. Grimes, who raised more than $5 million to challenge the senator, tied with or slightly ahead of Mr. McConnell. If that fall campaign materializes, it will be one of the most expensive and, probably, contentious in the country.

But behind his owlish glasses, Mr. McConnell appears utterly unperturbed. Somehow, he seems to be cruising.

On the surface, he has cause for worry. A New York Times/Kaiser Family Foundation poll in April put Mr. McConnell’s approval rating among Kentucky voters at 40 percent, compared with 56 percent for the Democratic governor, Steven L. Beshear. Mr. McConnell and Ms. Grimes were essentially tied, 44 percent to 43 percent, even after millions of dollars had been spent to prop up the senator’s standing and undermine Ms. Grimes.

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