The conflicting goals of President-elect Donald J. Trump’s economic agenda have been playing out as he debates who to choose as his Treasury secretary, a job that will entail steering tax cuts through Congress, leading trade talks with China and overseeing the $30 trillion U.S. bond market.

Budget experts have warned that his plans could add as much as $15 trillion to the national debt while increasing inflation and slowing growth. But Mr. Trump is not in the market for a naysayer. After a first term in which some of his top economic aides tried to tame his protectionist impulses, Mr. Trump is seeking a Treasury secretary who will carry out his unconventional plans while still having the credibility to keep markets buoyant.

That mix of qualities is not easy to find.

“I think Trump has a problem in that he wants two different things,” said Lawrence H. Summers, who served as Treasury secretary in the Clinton administration. “He wants somebody who will be deeply loyal, and he wants someone who will be deeply reassuring to markets. Since markets are fearful of the tariff agenda, it’s hard to square both things.”

In recent days, Mr. Trump has been considering several candidates for the job, and their prospects have been rising and falling by the hour, according to people familiar with the deliberations.

The current front-runners are Scott Bessent, the billionaire hedge fund manager, and Kevin Warsh, a former Federal Reserve governor. Marc Rowan, the chief executive of Apollo Global Management, is also in the running, while Howard Lutnick, Mr. Trump’s transition co-chairman who is the chief executive of Cantor Fitzgerald, appears to have fallen out of favor.