While he's no moderate, incumbent Sen. Mike Enzi has shown he is willing to compromise occasionally with Democrats, such as when he supported a sales tax on Internet purchases.
But Cheney, the elder daughter of former Vice President Dick Cheney, suggests that such compromise often isn't good enough for a true conservative.
"I'm running because I'm concerned about the direction of the nation," Liz Cheney said Tuesday. "I think it's time for us to say to ourselves, 'Can we continue to go along to get along in Washington?'"
Several Republicans senators elsewhere have faced tea party challengers questioning their conservative credentials. In Indiana, six-term Sen. Richard Lugar lost in a Republican primary last year to Richard Mourdock, who went on to lose to Democrat Joe Donnelly.
In Utah, tea party favorite Sen. Mike Lee ousted three-term incumbent Sen. Bob Bennett in 2010. And Sen. Orrin Hatch fended off a tea party challenger to win a seventh term last year.
The winner of Wyoming's Republican primary just over a year from now will be a heavy favorite to win the general election. Registered Republicans outnumber Democrats in Wyoming by a margin of more than 3 to 1.
Wyoming hasn't had a Democrat in its congressional delegation since 1979, the year Dick Cheney succeeded retiring Democratic Rep. Teno Roncalio to take the state's lone U.S. House seat.
Challenging any incumbent is a brazen move in Wyoming. At least until now, the state has shown considerable deference to those established in office.
Liz Cheney described herself as a tea party sympathizer. She called the movement favoring low taxes as a "force for good in terms of getting people focused on fiscal issues."
Liz Cheney, 46, is the older of Dick Cheney's two children, both daughters. Married with five children, she was a resident of Virginia until recently. She and her husband bought a home last year in the posh northwest Wyoming community of Jackson Hole.
Asked why voters should oust Enzi, a powerful incumbent, in favor of a rookie, Liz Cheney said seniority isn't necessarily an attribute.
"I think that part of the problem in Washington today is seniority," she told The Associated Press in a telephone interview. "I think it's time for a new generation, for a new generation to come to the fore. I don't see seniority as a plus, frankly."
Enzi announced he would seek re-election Tuesday, more than six months earlier in the political cycle than he has declared his bid in the past.
"Working behind the scenes - this is what I have been doing since I was elected, and this is what needs to be done," Enzi said by email through a spokesman.
He immediately won the endorsement of colleagues in the Senate, including the National Republican Senatorial Committee.
"Our support will be there for Mike," said the committee's chairman, Republican Sen. Jerry Moran of Kansas.
The other two members of Wyoming's congressional delegation, both Republicans, came out quickly in support of Enzi. Sen. John Barrasso and Rep. Cynthia Lummis praised Enzi for his long service and knowledge of Wyoming issues.
The race promises to be hard-fought. Enzi has had few serious Democratic challengers - much less Republican ones - since he was first elected to the Senate in 1996. He remains well-liked around the state as an affable former shoe salesman and mayor of the coal-mining city of Gillette.
Enzi, 69, takes pride in keeping a lower profile and remaining much less partisan than most of his colleagues. He often refers to his "80-20" rule - that opposing parties usually can agree on 80 percent of the details of any given issue - as a model for Republicans and Democrats to work together.
He handily won re-election in 2008 with more than 75 percent of the vote.
Liz Cheney's interest in the seat has been an open secret for months, dating at least to her purchase last year of a home in Wilson, a community in Jackson Hole, listed for $1.9 million.
She appeared onstage with her father at last year's state Republican Party convention. It was Dick Cheney's first public appearance since he underwent a heart transplant, and father and daughter have been working on a book together.
Since then, Liz Cheney has made frequent appearances at county-level GOP events in virtually every corner of the state. She also has been in the national public eye as a Fox News political commentator.
Wyoming political veteran Chris Rothfuss said Liz Cheney's candidacy might be a sign of the divisions that have roiled the national Republican Party for several years, with GOP officeholders being challenged from within their party if they are seen as too willing to compromise with Democrats.
Rothfuss, a Democratic state lawmaker who lost to Enzi in 2008, said Liz Cheney's challenge reflects "everything that's wrong" with partisanship in national politics.
"I would also say that the reason that Liz Cheney is running out of Wyoming rather than what in effect would be her home state of Virginia is because we're basically seen as a much cheaper option in trying to obtain a Senate seat," said Rothfuss, a chemical engineer.
But make no mistake, the Cheney family is well-established in Wyoming- an important qualification for anybody seeking major office in the state.
While Liz Cheney was born in Madison, Wis., her announcement pointed out that the Cheney family has roots that go back more than 100 years in Wyoming.
Liz Cheney holds a law degree from the University of Chicago and has worked as a lawyer for the State Department and the Agency for International Development.
Yet she said Wyoming always has been where her heart is.
"My sense is, as far the carpetbagger charge, is it's from people who don't want to talk about substance, don't want to talk about the issues," Liz Cheney said.
Donna Cassata and David Espo contributed to this report from Washington, D.C.