While Pompeo has indicated to McConnell that he would not take the plunge, a looming June 1 deadline and an increasingly difficult landscape for the GOP have added a new sense of urgency to the race.

Through a months-long advocacy campaign, McConnell successfully convinced the White House that the Kansas race is an issue for Republicans. And some people close to Trump are still pushing for Pompeo to get in and simplify things for the party, according to multiple people familiar with the situation.

Pompeo has been firm thus far that he will not reconsider and recently told the White House that he is not running. He declined to comment for this story. But ambitious politicians sometimes change their minds. Just this election cycle two Democrats, John Hickenlooper of Colorado and Montana Gov. Steve Bullock, have reversed themselves to run for Senate after consistently denying interest.