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."