GOP wonders: How high can Liz Cheney go?

Still, the outlines of her choice are clear. Staying in the House would maintain a Cheney family tradition — her father represented the state’s at-large district for a decade, rising to minority whip before leaving Congress to serve as defense secretary — and give her an excellent opportunity to someday become the first Republican female speaker.

But Cheney has eyed the Senate before, launching an abbreviated primary run against Enzi in 2014, and it’s the rare politician who prefers running every two years to every six years. Crossing the Capitol would also give Cheney, who served as a senior State Department official in the George W. Bush administration, a more prominent platform on national security. Her profile would undoubtedly exceed her status as the junior senator from the nation’s least populous state.

Another fact of political life: Not since Rep. James A. Garfield (R-Ohio) won election in 1880 has a sitting member of the House been elected president.

“She is on a shortlist of Republicans you can say with assurance will be at the top at some point, whether it’s in the House, the Senate or the White House,” said Josh Holmes, a former top aide to Senate Majority Leader Mitch McConnell (R-Ky). “She’s got a really unique set of skills and knows how to use them. My sense is that she is, at some point, going to be leading everything in D.C. It’s just a matter of from what perch.”