And the White House, in an unusual twist, openly disputed the budget office’s math.

Jason Furman, the chairman of the White House’s Council of Economic Advisers, said that the office’s estimate of the potential lost jobs might be too high. In a call with reporters, Mr. Furman said that finding no jobs effect at all would be a “perfectly reasonable estimate.”

The analysis does not reflect “the consensus view of economists,” he said. “Sometimes, you have to have respectful disagreement.”

But the report was embraced by leading Republicans, who have opposed the legislation despite its widespread popularity in public opinion polls. “Raising the minimum wage could destroy as many as one million jobs, a devastating blow to the very people that need help most in this economy,” said Senator Mitch McConnell of Kentucky, the minority leader. “If and when Democrats try to push this irresponsible proposal, they should be prepared to explain why up to a million Americans should be kept from having a job.”

Democratic lawmakers and liberal groups joined the White House in challenging that view. “I haven’t seen Republicans this excited about something that bucked the trend in their favor since the last poll showing Mitt Romney was about to be elected president,” said Brad Woodhouse, the president of Americans United for Change, a liberal advocacy group. “But sorry to rain on their parade — one report does not a trend make.”

The budget office found that lifting the federal minimum wage, currently $7.25 an hour, would have a complicated effect on the labor market, acting as a boon and a burden for businesses and workers.