Liz Cheney Elizabeth (Liz) Lynn CheneyOVERNIGHT ENERGY: Cheney asks DOJ to probe environmental groups | Kudlow: 'No sector worse hurt than energy' during pandemic | Trump pledges 'no politics' in Pebble Mine review Cheney asks DOJ to probe environmental groups Press: The big no-show at the RNC MORE is at a crossroads: Does she run for an open Senate seat in Wyoming that she’d be favored to win, or continue to climb the House leadership ladder with hopes of making history as the first female GOP Speaker?

Cheney, the No. 3 House Republican and the daughter of former Vice President Dick Cheney, has made no decision following Sen. Mike Enzi Michael (Mike) Bradley EnziChamber of Commerce endorses McSally for reelection Cynthia Lummis wins GOP Senate primary in Wyoming The Hill's Convention Report: Democrats gear up for Day Two of convention MORE’s (R-Wyo.) announcement that he will not run for reelection in 2020 after more than 20 years in the Senate.

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But a half-dozen House and Senate GOP lawmakers predict that Cheney will run for the upper chamber, where they say she would make an immediate and lasting impact on the issues she is most passionate about: defense and foreign policy.

Some of those GOP sources also said the Senate would be a much better launching pad if she ever decides to run for president. Also, past Speakers, including John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio) and Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.), typically last only a few years in the job, while senators can serve decades.

“I predict she runs. It’s hers if she wants it,” said a House GOP colleague who works closely with Cheney. “Senators can really shape policy.”

Conservative Rep. Scott DesJarlais (R-Tenn.), who serves with Cheney on the House Armed Services Committee, called her whip-smart, well-prepared for hearings and well-versed in institutional knowledge.

“I think she would make a great senator,” DesJarlais told The Hill.

“The growth of influence for her if she runs for the Senate is dramatically steeper than climbing the House ladder,” added a Republican senator who earlier made the jump from the House.

Cheney, who was elected chairwoman of the 197-member House Republican Conference last fall, has a lot of factors to consider. A new internal rule forces members of leadership and committee chairs to step down once they announce a bid for higher office, so Cheney would need to relinquish her prized leadership post if she jumps in — a move that would set off a scramble among other ambitious House lawmakers.

But GOP sources said it’s unlikely Cheney is feeling any pressure to make a hasty decision; because of her front-runner status, she has essentially frozen the field of potential candidates. And the Senate filing deadline is not until May 28, 2020, with the Wyoming primary set for Aug. 18, giving Cheney ample time to decide on her future.

Others noted that there is a path for Cheney to attain the Speaker’s gavel, even if it’s not as clear as her road to the Senate. House Minority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy threatens motion to oust Pelosi if she moves forward with impeachment Kate Schroder in Ohio among Democratic challengers squelching GOP hopes for the House McCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother MORE (R-Calif.), 54, and Minority Whip Steve Scalise Stephen (Steve) Joseph ScaliseHouse GOP slated to unveil agenda ahead of election House panel details 'serious' concerns around Florida, Georgia, Texas, Wisconsin elections Scalise hit with ethics complaint over doctored Barkan video MORE (R-La.), 53, are ahead of Cheney in the pecking order. But as the highest-ranking GOP woman in Congress, Cheney — an effective communicator and a member of one of the most powerful families in Washington — could possibly leapfrog both men in the event of a knock-down, drag-out fight between McCarthy and Scalise in 2020 or 2022.

“Opinion is divided. Many think she believes she is on the short track for Speaker, so why go to the Senate and be a back-bencher?” a third GOP House lawmaker told The Hill. “Remember, her dad was a House guy through and through.”

Dick Cheney, who like Liz Cheney served as Wyoming’s at-large congressman and House Republican Conference chair, went on to become House GOP whip and George H.W. Bush’s Defense secretary before he was tapped as George W. Bush’s vice president.

“There’s really no real wrong decision,” said a Republican operative. “She’s going to be in a good spot either way, either rising up the House leadership ranks with potentially [becoming] Speaker, maybe in the near future, maybe down the road, or joining the Senate in becoming a sort of leading voice on foreign policy and especially joining the folks like Joni Ernst Joni Kay ErnstThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Romney backs pre-election Supreme Court vote, paving way for McConnell, Trump MORE as a strong female voice for Republicans in the upper chamber.”

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While Cheney, 52, would be the clear front-runner to win Enzi’s Senate seat in deep-red Wyoming, she’s not the only Republican being floated. Former Wyoming Gov. Matt Mead, 57, has been mentioned as a potential candidate. Former Rep. Cynthia Lummis Cynthia Marie LummisChamber of Commerce endorses McSally for reelection Cynthia Lummis wins GOP Senate primary in Wyoming Chamber of Commerce endorses Ernst for reelection MORE (R-Wyo.), 64, whom Trump had interviewed for Interior secretary, is another potential candidate; she had been a member of the hard-right House Freedom Caucus and is beloved by conservatives.

“Cheney would be a great addition to the Senate, but regardless of who runs this will be a Republican seat,” another GOP strategist said.

A veteran of Senate campaigns called Cheney “very highly regarded on the Senate side and the race would be a cakewalk for her. Lots of folks are really hoping she decides to move up a chamber.”

A Senate seat has been appealing to Cheney in the past. She challenged Enzi in the 2014 GOP primary, prompting the low-key senator to inform reporters that Cheney, a Fox News commentator and former State Department official, had lied when she had promised she would not challenge him.

“I thought we were friends,” Enzi said at the time.

But the Wyoming political establishment rallied to Enzi’s defense, forcing Cheney to drop her bid. She won Wyoming’s at-large congressional seat in 2016, after Lummis retired from the House.

Asked about Cheney possibly running for his Senate seat, Enzi — after a long pause — told The Hill, “I’m really disappointed anyone is trying to talk to me about succession. I got a year and a half around this place. So I’m still enjoying the fact that I just said that I’m not running again.”

Despite Cheney’s history with Enzi, a person familiar with the two officials said they have mended any past divisions and established a very productive working relationship. Cheney swiftly released a statement following Enzi’s retirement announcement that strongly praised the senior senator from Wyoming.

In his retirement announcement over the weekend, the 75-year-old Enzi seemed to suggest that Cheney’s future is in the House.

“I’m leaving the Senate and House in good hands since John and Liz are in leadership,” Enzi said. “I can see a future when Representative Cheney will be the Speaker of the House and Senator [John] Barrasso will be the Senate Majority Leader.”

Barrasso (Wyo.), who is the third-ranking Senate Republican, said Monday he “is looking forward to working with [Cheney] in whatever she chooses to do. And we will hold the Republican Senate seat in Wyoming, regardless of who our candidate is, but she’s terrific.”