WASHINGTON — Raising the federal minimum wage to $15 an hour — a proposal included in the package of relief measures being pushed by President Biden — would add $54 billion to the budget deficit over the next decade, the Congressional Budget Office concluded on Monday.

Normally, a prediction of increased debt might harm the plan’s political chances. But proponents of the wage hike seized on the forecast as evidence that the hotly contested proposal could survive a procedural challenge under the Senate’s arcane rules.

Democrats are trying to add the measure to a $1.9 trillion pandemic relief package that is advancing through a process called budget reconciliation, which requires a simple majority rather than the 60-vote margin to overcome a filibuster. But reconciliation is reserved for matters with a significant budgetary effect.

Senator Bernie Sanders, the Vermont independent, said the forecast of an increased deficit showed that the measure passed the test. Raising the federal minimum wage to $15 “would have a direct and substantial impact on the federal budget,” he said in a statement. “What that means is we can clearly raise the minimum wage to $15 an hour under the rules.”

Critics of the plan noted a different element of the report: its forecast that raising the minimum wage to $15 would eliminate 1.4 million jobs by the time the increase takes full effect.

“Conservatives have been saying for a while that a recession is absolutely the wrong time to increase the minimum wage, even if it’s slowly phased in,” said Brian Riedl, a senior fellow at the Manhattan Institute. “The economy’s just too fragile.”

He also contested Mr. Sanders’s argument that the study raised the odds that a wage increase could survive Senate rules. The study found the measure would affect private-sector wages much more than it would raise the deficit — $333 billion versus $54 billion — showing its effect on the deficit was incidental, Mr. Riedl said.

“I doubt the parliamentarian will determine that this is primarily a budgetary reform rather than an economic reform with a secondary budget effect,” he said.

The rules say the budgetary effects cannot be “merely incidental” but do not define the phrase. While Mr. Sanders called $54 billion substantial, Mr. Riedl said it was about half of 1 percent of the projected 10-year deficit.

Congress last passed a minimum-wage increase in 2007. The current federal minimum, $7.25 an hour, is about 29 percent below its 1968 peak when adjusted for inflation, according to the left-leaning Economic Policy Institute. David Cooper, an economic analyst at the institute, said 29 states and the District of Columbia have higher minimums, and seven states plus the District of Columbia were phasing in the $15-an-hour threshold.

Progressives see the wage increase as a central weapon for fighting poverty and inequality, while conservatives often warn it will reduce jobs.

The report in essence said both sides were right. It found a $15 minimum wage would offer raises to 27 million people and lift 900,000 people above the poverty line, but it would also cost 1.4 million jobs.

Mr. Cooper disputed the jobs forecast, arguing that it was out of line with recent studies that showed increases in the minimum wage had produced little or no effect on employment. “C.B.O. seems to be going in the opposite direction,” he said.

Progressives like Mr. Sanders have been arguing that an increased minimum wage would reduce federal spending because fewer people would need safety-net programs like food stamps or Medicaid. But the budget office warned that those savings would be more than offset by the higher costs of delivering services like medical care, as employers raised their workers’ pay — a finding Mr. Sanders continued to reject, citing other studies.

On balance, the report said the changes would benefit labor over capital.

“They assume that there is income transferred from workers at the top of the income distribution to workers at the bottom,” Mr. Cooper said. “Therefore, they implicitly say that the minimum wage is a tool for fighting inequality. That’s probably the most explicit they’ve ever been on that point.”