BoehnerJohn BoehnerLobbying World 'Ready for Michelle' PACs urge 2020 run News Flash: Trump was never going to lock Clinton up MORE shot back with a tongue-in-cheek reply questioning whether additional contributions were on the way shortly.
Several Republicans who attended the dinner saw that as a lighthearted way to reference a feeling that Stearns has not given enough to Republicans during his more than two decades on Capitol Hill.
"The joke is that it's a down payment for everything he's owed for the past 20 years," said a senior Republican House aide.
Several senior GOP House staffers said they are not sure Stearns's fundraising record will impress the committee when Republicans who brought in more more money are also raising their hands for the spot.
Rep. Fred Upton (R-Mich.) is cited by many GOP aides and lobbyists as a leading contender for the position.
A spokesman for Upton told the Hill that it is his boss's "goal to be to the next chairman."
"Fred is unparalleled with his combination of seniority and demonstrated leadership on the Committee," Sean Bonyun, the spokesman, said.
"The utmost priority right now is to regain control of the House and Fred is aggressively working to elect Republican candidates across the country," he added.
Upton has better fundraising credentials than Stearns. He has transferred over $700,000 to the National Republican Congressional Committee this year, compared to Stearns' $520,000, according to a senior GOP aide.
Upton, ranking member of the Energy and Environment subpanel, co-chaired the NRCC March fundraising dinner that brought in $7.2 million, a record for the annual event. He is also a more-senior member than Stearns, another factor that could influence the votes of the steering committee.
Rep. John Shimkus (R-Ill.) is also sometimes cited as a contender for the top Energy and Commerce slot.
"Congressman Shimkus is focused on electing John BoehnerJohn BoehnerLobbying World 'Ready for Michelle' PACs urge 2020 run News Flash: Trump was never going to lock Clinton up MORE Speaker of the House and other issues come after that," said a spokesman for Shimkus.
Unlike Stearns or Upton, Shimkus is a member of the steering committee that votes on the matter on behalf of his region of the country.
He has raised less money for the NRCC this year ($315,000) and is less senior than Stearns or Upton.
Still, Republicans noted that fundraising and seniority are not the only considerations for the steering committee. A members' political views also play a role.
Leaders may want a staunch Republican in the position in order to make the committee a conservative bastion that will fight back against Democratic initiatives such as the healthcare law. Upton is viewed as more moderate than Stearns or Shimkus, but he has nevertheless earned strong respect from industry groups impacted by the committee.
The committee's ranking member, Barton, cannot become chairman unless he obtains a waiver to override term limits imposed by GOP rules. His controversial remarks about BP, which were interpreted as sympathetic to the company, could make the waiver a tougher get.