Anyone who wants to succeed Rep. Liz Cheney in leadership should be careful what they wish for, because her current post is traditionally a dead end.

The chair of the House Republican Conference, the No. 3 spot in the hierarchy, has served to either end political careers or force lawmakers to abandon the leadership ladder to reinvent their résumé in other offices.

No Republican has ascended directly upward in leadership ranks since Rep. Richard K. Armey (Tex.), after a brief stint as conference chairman, did so more than 26 years ago following a wave election that swept the GOP into the House majority.

Democrats have a similar ceiling from the equivalent position in their ranks, known as chair of the Democratic Caucus.

The Fix’s Aaron Blake breaks down the growing momentum among House Republicans to oust Rep. Liz Cheney (R-Wyo.) from leadership and what it means for the party. (JM Rieger/The Washington Post)

Over the past 30 years 10 Democrats held that leadership spot, and just one, Rep. James E. Clyburn (S.C.), moved directly up in leadership, after less than a year in the job and a similar wave for Democrats that swept them into power in 2006.

No one can fully explain why each party places so little value in this leadership post.

Democrats have a four-year limit on the chair and vice chair of the caucus, creating an up-or-out system and more churn.

And Republicans have a knack for blaming their conference chair when things go wrong, as senior members of leadership deflect blame and let the rank and file take out their anger on a lower-level member of leadership.

These two leadership jobs have vague responsibilities: running a weekly closed-door meeting of the caucuses, overseeing a news conference and managing a staff that helps shape the respective party’s message.

It’s the type of job that often gets notice only when something goes wrong.

To be sure, some have bounced into greener political pastures, most notably John A. Boehner (R-Ohio), who became House speaker 12 years after he was ousted as conference chair, and Mike Pence, who went on to be Indiana governor and vice president after his one term as conference chairman. Rahm Emanuel (Ill.) went from House Democratic Caucus chairman to White House chief of staff and then Chicago mayor.

Now both sides are going through another round of musical chairs in these posts, with the futures of once rising stars coming to a head.

Republicans are first up in making another move. On Wednesday, when Cheney (Wyo.) convenes the House Republicans for their first meeting in three weeks, some GOP lawmaker is expected to make a motion to expel her from that post after just two years and four months in the job.

After the 2020 elections and the Jan. 6 insurrection at the U.S. Capitol, Cheney has repeatedly spoken out against former president Donald Trump and called for the party to move on, an apostasy inside a group where he is still considered very popular.

House Minority Leader Kevin McCarthy (Calif.) initially supported Cheney, but as he came under increasing pressure from Trump and his conservative flank, McCarthy has signaled he wants her ousted and has privately thrown his support to Rep. Elise Stefanik (N.Y.).

Stefanik, 36, in her fourth term, was once considered a rising star of the Republican establishment but has instead adopted Trump’s “America First” tone, winning an endorsement from the former president.

“I’m committed to being a voice and sending a clear message that we are one team, and that means working with the president and working with all of our excellent Republican members of Congress,” she said Thursday on a Trump-friendly podcast.

If she wins, Stefanik would become the sixth GOP conference chair in 13 years — a turnover rate that rivals the drummer for Spinal Tap.

Rep. Hakeem Jeffries (N.Y.), the Democratic Caucus chairman, is a lame duck, hitting his term limit at the end of 2022.

For more than 15 years, the trio of House Speaker Nancy Pelosi (Calif.), Majority Leader Steny H. Hoyer (Md.) and Clyburn, the majority whip, have been atop the caucus in positions without term limits.

Pelosi and Hoyer, both 81, have served in the top two posts since 2003, making Jeffries the seventh caucus chair in that tenure.

After leaving Congress in late 2008, Emanuel spent two years as President Barack Obama’s chief of staff, eight years as Chicago mayor, two more in retirement, and he is now under consideration by President Biden to be ambassador to Japan — and in the House, Pelosi, Hoyer and Clyburn are still running the show.

In a survey of senior Democratic aides, Punchbowl News found that Jeffries, 50, was the clear favorite to succeed Pelosi, with the expectation of a total generational shift with her, Hoyer and Clyburn stepping aside.

But no one knows when that day will come, other than those three octogenarians.

“I don’t have any intention of declaring myself a lame duck,” Pelosi said during a “PBS NewsHour” interview, when she was reminded that she originally said she would serve as speaker through next year.

She mentioned her family and said “I fully intend,” but then paused and just said “we want to do some great things in this election.”

Jeffries became caucus chairman only after then-Rep. Joseph Crowley (N.Y.) lost his 2018 primary as he had been attempting to use that post to build his national brand in a not-very-subtle attempt to succeed Pelosi.

After a disappointing 1998 midterm election, Boehner got bounced out as GOP conference chairman as more senior Republicans fed him to a rank and file hungry for more change.

He went on to become a committee chairman, then back into leadership in 2006 and took over as the top Republican the next year, serving as House speaker from 2011 to 2015.

In his new memoir, Boehner acknowledged that the conference leadership post was not super powerful, but he saw it as a way to build his credibility with the more conservative wing. So he used his influence to steer then-Reps. Pence (Ind.) and Jeb Hensarling (Tex.) into that leadership job in 2009 and 2011, respectively.

“It was better to have talented members with a rabble-rousing streak working with you rather than against you,” Boehner writes in “On the House.”

Both quickly realized they did not have much clout. Pence left after 2010 — even though Republicans had just seized the majority — because he wanted to run for governor of Indiana and thought it would be easier to do outside of leadership.

Hensarling, who took over for Pence and never took to the job, became the third straight one-term conference chair, jumping ship to become chairman of the Financial Services Committee.

Cheney entered the GOP position in January 2019 with much fanfare. She had aggressively pushed aside Rep. Cathy McMorris Rodgers (Wash.), who served six years in that leadership spot, the longest in either caucus in more than 30 years, and Republicans considered Cheney to be on the path to become the first Republican woman to serve as House speaker.

That talk barely lasted two years, and now Stefanik is the rising star of the moment, likely to take over as conference chair.

History suggests that star will very soon have to move elsewhere to keep on shining.