Former Hillary Rodham Clinton aide Cheryl Mills, left, listens as House Select Committee on Benghazi Chairman Trey Gowdy (R-S.C.) speaks to reporters on Capitol Hill in Washington on Sept. 3. (Susan Walsh/AP)

Whispers are everywhere that South Carolina Rep. Trey Gowdy will enter -- or be drafted into -- the race to be House majority leader, the second most powerful job in the Republican-controlled House. And Republicans (at least those in Washington) should be rooting like crazy for that to happen.

Here's why: As I noted yesterday, changing out John Boehner as speaker for Kevin McCarthy as speaker (McCarthy is currently the majority leader) isn't much of a change. Yes, McCarthy is younger and might be slightly more well-regarded among the younger and more conservative elements of the party than was Boehner. But  that's not saying much. And no one would mistake McCarthy as of the tea party base. He's an institutionalist who is likely to face lots of the same challenges that led Boehner to call it quits.

At the moment, the choices to replace McCarthy as majority leader are Rep. Tom Price (Ga.) and Rep. Steve Scalise (La.). Scalise is currently  majority whip; Price is the chair of the Budget Committee. Both are well-liked by conservatives -- and got their starts from the conservative sinecures within the GOP conference. But both are already in prominent positions and neither is all that skilled as a television performer -- a trait considered essential to jobs in leadership these days. (Scalise was also recent enmeshed in a controversy over his having appeared in front of a white supremacist group in the past.)

Gowdy is all the things Price and Scalise are not. He's a regular -- and a star -- on Fox News Channel thanks to his job as chairman of the House select committee investigating the attacks in Benghazi, Libya, on Sept. 11, 2012. He's seen as the latest (and best) iteration of the tea party movement in Congress, someone who is committed to core conservative principles but is also adept at knowing which levers of power to pull when. (Gowdy is a former federal prosecutor.)

"If you want the best person to make the Republican case, if you want the best person to talk about why conservatism is the right answer for America, Trey Gowdy is our best foot forward,” Utah Rep. Jason Chaffetz said during an interview on Fox News Channel on Tuesday morning.

The only way that the new Republican leadership will have a better chance of success than the Boehner regime achieved is if, somehow, they can find ways to bring the 30 (or so) tea party conservatives into the fold on key votes. Boehner, McCarthy and Scalise (the last who was brought on to the leadership team, at least in part, to placate conservatives) were never able to do that. Gowdy has a credibility with the hardcore tea party element that none of the current leadership team carries.

There's no guarantee that Gowdy runs or, if he runs, that he would win the post, since both Scalise and Price have been working far more aggressively to court support. There are also conflicting reports as to whether Gowdy will run, won't run but will allow himself to be drafted or will do neither. (We'll know more after the big Republican confab tonight -- a "where are we and where are we going" conversation pushed for by Illinois Rep. Peter Roskam.)

And, there's no guarantee that even if Gowdy did run and win a spot as the No. 2-ranking Republican that he would be able to fundamentally alter the dynamic that has governed the Republican conference since the party took over in 2010 -- a schism between an establishment who sees compromise as a necessity and a rump group who views it as capitulation.

Electing Gowdy wouldn't change anyone's beliefs on either side of that split. But  trust is a critical component in politics, particularly in a legislative body like the House. And having someone they trust in leadership might well convince the tea party wing to play ball with the establishment, at least some of the time.

For a party whose last five years ruling the House has been defined by its inability to, well, rule the House, something needs to be changed if different results are to be reasonably expected. Simply shuffling the leadership slots among the same cast of characters isn't real change. But will the GOP leadership and rank and file recognize the long-term (and even short-term) good that elevating Gowdy could do for them?