WASHINGTON - After toppling three-term Republican Sen. Robert F. Bennett in Utah, tea party activists and other conservative critics shifted their sights Sunday to a mid-May primary in Kentucky, their next big challenge to a political establishment they have vowed to upend.

Bennett, 76, left the door open to a write-in campaign after losing his bid for renomination, raising the possibility of an unpredictable three-way race that could yet extend his career.

But within minutes of Bennett's defeat, the chairman of the Republican senatorial campaign committee, Sen. John Cornyn of Texas, announced the organization will support the winner of a June 22 primary between businessman Tim Bridgewater and attorney Mike Lee.

Republicans are heavily favored to hold the seat in the fall in a state that hasn't elected a Democratic senator in more than three decades.

In his home state, Republicans said Bennett's defeat raised questions about the political future of Utah Sen. Orrin Hatch, also a conservative, who may face a challenge from GOP Rep. Jason Chaffetz in 2012.

Hatch has worked to protect his conservative flank carefully in the past year. His opposition to Supreme Court Justice Sonia Sotomayor was the first time in a career of more than 30 years that he voted against a high-court nominee, and he pulled out of last year's bipartisan talks on health care legislation shortly after they began.

Nationally, the events at the Salt Palace Convention Center in Salt Lake City marked a key moment in the struggle roiling Republicans, the demise of a veteran conservative, influential in the party's inner councils in the Senate, tossed out in large measure because he voted for the financial bailout legislation of 2008.

"The whole reason I started the tea party (in Utah) was Sen. Bennett. He was the next one up for election," said David Kirkham, who added that his opposition developed after the veteran lawmaker voted for the bailout President George W. Bush sought in late 2008.

Other critics said they were unhappy that Bennett had co-sponsored bipartisan legislation that would have required individuals to purchase health insurance, and noted he had once pledged to serve only two terms.