“Making sure that Boeing is strong again is very, very powerful and very important, and we’ll do whatever is necessary to do,” Mr. Trump said on Friday at a briefing on the government’s coronavirus response. He noted that the company “has not asked for aid yet, but I think they probably will.”

Yet as negotiations over the stimulus heated up late last month — with Boeing officials working closely with the White House and key members of Congress to communicate the company’s needs and preferences — Mr. Calhoun gave an interview that provided fodder to critics, left supporters puzzled and created confusion among government officials involved in the negotiations.

Mr. Calhoun suggested in an interview with the Fox Business host Maria Bartiromo last month that Boeing would not accept taxpayer money if it meant giving the government a stake in the company, a condition that was being debated at the time as part of the federal bailout legislation working its way through Congress. The final legislation included conditions for some of the aid, including the possibility of the government taking an equity stake and limits on layoffs and stock buybacks.

“I don’t have a need for an equity stake,” Mr. Calhoun said in the interview. “If they force it, we just look at all the other options, and we’ve got plenty of them.”

He added, “If they attach too many things to it, of course you take a different course.”

The comments prompted a flurry of phone calls from members of Congress to Boeing executives and lobbyists, according to people familiar with the exchanges.

Was Mr. Calhoun saying that the company didn’t want to be included in the bailout, or that its internal prognosis was better than the company’s debt-laden balance sheet suggested?

The responses from the company’s lobbyists to lawmakers were emphatic, if at odds with Mr. Calhoun’s pronouncement: Yes, Boeing needed the federal money, and no, it was not in better shape than it looked. Internally, Mr. Calhoun’s colleagues informed him that he had sent the wrong message, according to two people familiar with the matter.