(CNN) -- The U.S. Senate race in Wyoming has it all: A popular incumbent Republican facing a primary challenge, a GOP feud, a generational divide, and Dick Cheney, one of the most polarizing figures in politics.
Liz Cheney met with reporters in Casper on Wednesday, one day after announcing her bid for the seat. It came on the same day that three-term Republican Sen. Mike Enzi said he would run for re-election.
"I'm focused on earning every vote I can, the way it ought to be done in Wyoming, which is one person at a time," Cheney said.
Cheney, a former State Department official and Fox News contributor, is the eldest daughter of the former vice president, who served for a decade as the congressman from Wyoming.
Like her father, Cheney is a very vocal critic of President Barack Obama.
"President Obama has launched a war on our Second Amendment rights. He has launched a war on our religious freedom. He has used the IRS to launch a war on our freedom of speech. He has used the EPA to launch a war on Wyoming's ranchers, farmers and energy industry," said Cheney in a statement announcing her bid.
CNN Chief National Correspondent John King, who covered the Cheneys over the years, says Liz Cheney has been a very loyal aide to her father.
"Clearly she has his blessing or she wouldn't do it," King said. "If her dad had turned to her and said 'Don't do this,' she wouldn't have done this. In her putting her neck out, in her offending Mike Enzi and everyone else in the Wyoming Republican party, so has her dad."
Enzi is a proven conservative but has been willing to try to accomplish bipartisan solutions in the Senate.
While not directly criticizing him in her announcement, Cheney said, "I am running because I know as a mother and as a patriot, we can no longer afford simply to go along to get along."
And the 46-year-old Cheney appears to be making Enzi's age an issue, saying, "I believe it is necessary for a new generation of leaders to step up to the plate."
Enzi is 69.
One veteran analyst of Senate races isn't sure the age argument will be effective.
"She is running against an incumbent from her own party who has a solidly conservative voting record and is well-liked by voters. Her theme seems to be Enzi's age, but I don't know that it will play that well," said Jennifer Duffy, senior editor for the non-partisan Cook Political Report.
But the primary will highlight the ongoing struggle for the future of the GOP.
"This race now will be the highest-profile test of what's happening in the Republican Party, the struggle over whether you fight and compromise or do you fight and keep fighting. This race will capture huge national attention," King added.
Enzi says he's not surprised he's being challenged.
"She's been traveling around Wyoming for a long time, so I'm not surprised. I'm only surprised in that she said if I ran she wouldn't. She announced 30 minutes after I more specifically stated my intention," Enzi told CNN Chief Congressional Correspondent Dana Bash on Wednesday.
And he pushed back on his age, telling Bash, "I'm absolutely not too old to be a senator. I'm about the median age for this body. I'm in really good health, I'm on the committees that I want to be on. I have seniority."
And Enzi doesn't think his ability to work with Democrats is a liability, saying "I've developed trust on both sides of the aisle, people trust me that what I say I'm going to do, I do."
On Tuesday Enzi told reporters that he wouldn't change his plans to run for a fourth term, but admitted to reporters that fundraising has "always been a problem for me."
But he told Bash that people in Wyoming "complain about long campaigns. It doesn't take them long to make up their mind. And it doesn't cost a lot of money to have them make up their mind."
Enzi appears to have the backing of the two other members of Wyoming's congressional delegation.
"I think that Mike has done an excellent job representing the people of Wyoming and I'm going to continue to work to support Mike Enzi, Sen. John Barrasso told CNN on Wednesday.
"I have a great deal of respect for the entire Cheney family, for the vice president, for Liz and for Lynn, but I think it's the wrong race at the wrong time," he said.
Republican Rep. Cynthia Lummis of Wyoming ripped Cheney's decision as "bad form" and predicted she would lose in the GOP primary next year.
"I don't know that anybody can out-conservative Mike Enzi," Lummis told CNN Senior Congressional Producer Deirdre Walsh and other reporters outside the House chamber on Tuesday.
The congresswoman, Wyoming's at-large representative, admitted Cheney had the upper hand in raising money, but said that wouldn't matter.
"She will outraise him by factors of 10 or more, and he will still win because Wyoming is grassroots, retail campaigning," she said.
The National Republican Senatorial Committee was quick to say it stands firmly behind Enzi, the GOP incumbent.
"Our mission is to re-elect our incumbents and build a Republican majority," NRSC Communications Director Brad Dayspring told CNN.
Cheney, who chairs a nonprofit on national security and education called Keep America Safe, had been rumored this year to be considering a Senate run.
Early last week, former Sen. Alan Simpson of Wyoming told the New York Times that a potential Cheney primary challenge would bring about "the destruction of the Republican Party of Wyoming," adding that, "It's a disaster -- a divisive, ugly situation -- and all it does is open the door for the Democrats for 20 years."
Simpson had a different message after Cheney's announcement on Tuesday.
"I deeply care about them both," he said, according to the Casper Star Tribune.
Cheney will come under attack for being a carpetbagger. She was born in Wisconsin and grew up in Virginia's D.C. suburbs before attending college in Colorado and law school in Illinois. She spent most of her career working in the nation's capital before moving to Wyoming last year.
Cheney touted her family's longtime Wyoming roots in a speech in May and in her announcement Tuesday.
He highlighted that her family "first came here in 1852, in search of religious freedom," adding that her grandmother "was raised in the Salt Creek oil field and grew up to become Natrona County's first female deputy sheriff."
Will the carpetbagger tag stick?
There have already been comparisons to Hillary Clinton. In 2000 the first lady, who grew up in Illinois and lived for many years in Arkansas, successfully ran for the U.S. Senate in New York, but faced the carpetbagger attacks.
"What did Hillary Clinton have? She had national name identification. She had a giant fundraising network, she had a bunch of people willing to work for her and willing to fight and she ran a very effective campaign and she won," King recalled.
As for Cheney, he said, "She will have money. She has the name identification. Now the test is, since she's new to politics, can she run a campaign. Can she convince the people of Wyoming that she's right."
CNN's Kevin Liptak, Ashley Killough and Bryan Koenig contributed to this story