Liz Cheney to challenge Sen. Mike Enzi, R-Wyo.

Updated at 7:55 p.m. ET

Liz Cheney, the daughter of former Vice President Dick Cheney, will run against longtime Sen. Mike Enzi, R-Wyo., CBS News has confirmed. Cheney launched her campaign Tuesday following Enzi's announcement that he'll run for a fourth term.

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"Instead of cutting deals with the president's liberal allies, we should be opposing them, every step of the way," Cheney said in her announcement video. "This is our state and our country, we don't have to accept what Washington, D.C., is doing for us."

Cheney, a Fox News political analyst, has recently ramped up her speaking engagements with the Republican Party in Wyoming. Enzi learned Cheney was considering entering the race when she called him last week, the New York Times reported.

Rep. Cynthia Lummis, R-Wyo., who said recently she was considering a run if Enzi retired, blasted Cheney as a carpetbagger who will wind up losing to Enzi, even though she'll "outraise him by factors of 10 or more."

"When somebody's never gotten a paycheck in Wyoming and lived their whole adult life in Virginia, I think they should run for Virginia. That's her home state," Lummis said.

Enzi entered the year as an overwhelming favorite for re-election. In Enzi's last general election race in 2008 he coasted to victory, with three-fourths of the vote. Most of Wyoming's voters at the time called themselves Republicans, so the voter pool in a GOP primary here is fairly large relative to the state. At the time Enzi showed no trouble at all with conservatives, winning almost all of them, and he's steered a very conservative course in the Senate since.

Sen. Rand Paul, R-Ky., a popular figure in GOP circles, has stated his support for Enzi. The state is reliably Republican enough that whoever takes the GOP nomination would be an extremely heavy favorite in the general election. Still, as with many party primaries some will wonder if such a challenge will stir echoes of 2010, when nomination fights within the GOP might have cost candidates in the general, or draw attention to larger rifts in the party.

Money may be a factor, and Cheney will surely tap her father's sources, but this is not an expensive state in which to campaign, which could mitigate that issue.

CBS News' Jill Jackson contributed to this report.