“There’s a very real possibility we will win a race for Senate in Florida and lose a race in Texas for Senate, O.K.?” Mr. Mulvaney said. “I don’t think it’s likely, but it’s a possibility. How likable is a candidate? That still counts.”

And Mr. Mulvaney alluded to last year’s special election for Senate in Alabama and suggested that Mr. Trump remained bewildered at his party’s defeat there. The Democratic nominee, Doug Jones, prevailed in a stunning upset over the Republican, Roy Moore, a polarizing former judge who was accused of once preying on teenage girls.

“The president asks me all the time, ‘Why did Roy Moore lose?’” Mr. Mulvaney said. “That’s easy. He was a terrible candidate.”