Mike Pompeo has a new badge he has been handing out to students and aspiring diplomats in the midwest. “United States Department of State” it says around the outside, with the word SWAGGER stamped in red capitals diagonally across the middle.

In the background, printed in pale blue like subliminal messages are a list of attributes, such as “patriotic”, “confident”, “respected” as well as “cool vibe”.

In the state department right now the vibe is anything but cool, and Pompeo’s dogged insistence on making “swagger” a catchphrase has become the punchline to a thousand wry jokes in Foggy Bottom.

These buttons were just passed out to students. pic.twitter.com/YnZ9gYQ1w8 — kylie 🌻 (@kcylizzle) October 25, 2019

With foreign service officers being summoned daily to testify in the Ukraine impeachment hearings, while being denounced by the White House as “radical unelected bureaucrats” for doing so, and with the US being lambasted for deserting its Kurdish allies in Syria, Pompeo’s staff have questions on why he is handing out “swagger badges” and why he is doing it in Kansas.

He spent half of last week in his home state, attending events on “workplace development” with Ivanka Trump. Pompeo suggested it was all part of being secretary of state, arguing that “if we are not able to build hi-tech, innovative products, then my capacity to execute American diplomacy around the world will be diminished”.

To many – in Kansas and beyond – that looked like a stretch. The badges, glad-handing and posing with Ms Trump seemed more like someone lining up his next job, particularly as it coincides with one of the state’s Republican senators stepping down.

It was Pompeo’s fourth visit to the midwestern state so far this year, and more than one in seven of the nearly 200 interviews he has given in 2019 have been to Kansas-based media outlets. It was also reported by the Wall Street Journal, that he took time in Wichita to meet Charles Koch, his longstanding sponsor and a kingmaker on the right of Republican party.

Three of Pompeo’s trips to Kansas have been official visits paid for by the state department, leading Democrats to file a complaint that he is violating federal laws prohibiting political activities while acting in an official capacity.

Pompeo dismissed the complaint as “silliness”.

“It’s the kind of left-coast, elitist liberalism that can’t understand how someone would want to go to the amazing place like Kansas,” Pompeo said on Friday in yet another interview with a Kansas-based radio station.

If Pompeo is not running for the Senate, the Kansas City Star noted irritably, he had “better things to do” than to keep coming back. And if he did really want to run “then he should quit his rather important day job and do that”.

Pompeo’s exit from the state department would be a dramatic development. Since the departure of James Mattis from the Pentagon and John Bolton from the National Security Council, he is the most powerful member of the cabinet, though his views can still be swept aside by an impetuous president.

The secretary of state does not have to make up his mind whether to abandon ship for some time. Registration does not close for the Kansas Senate race until June next year, and he could arrive late in the Republican primary and still dominate. He has $1m in campaign funding left over from when he was a Kansas congressman, and he has Koch at his back along with other deep-pocketed donors.

“If Pompeo comes in, it would be no contest,” said David Kensinger, a Kansas Republican political consultant. “His affiliation with the president will only help him, and no Republican has lost a Senate race in Kansas since 1932.”

Burdett Loomis, professor emeritus in political science at the University of Kansas, argued that the longer the impeachment process, the Syrian fiasco and other Trump travails continue, the more they would weigh down a Pompeo Senate candidacy.

“Four or five months ago, he would simply be able to walk in here and big-foot his way into the nomination. Right now, I think it’s somewhat less likely,” Loomis said. “Even though Kansas is a certainly Republican state or red state, it’s never been one that has been wildly enthusiastic about Trump.”

Like Kensinger, Loomis did not think Pompeo had made a definite decision to run, but was keeping his options only. Russell Arben Fox, political science professor at Friends University said Pompeo was “a very disciplined, methodical person, who doesn’t do abrupt shifts”.

“As long as Trump doesn’t fire him or throw him under the bus in the impeachment process, I don’t think he would leave,” Fox said. “What is the advantage to him politically?”

Thomas Wright, the director of the Centre on the US and Europe at the Brookings Institution, suggested that the flirtation with a Kansas Senate run could even be a feint, designed to remind Trump he has other options, to help the secretary of state get his way in internal disputes.

“I remain doubtful that he wants to be in Congress again. I don’t see why it is a better launching platform for a 2024 bid (better to be outside the Beltway),” Wright said, predicting Pompeo would step down after next year’s elections and go back into business. “I suspect he may want the compensation that goes with the private sector.”