The idled workers would be disproportionately younger and less educated, and CBO projects that half of them would drop out of the labor force. Prices would also rise for goods and services that rely on entry-level labor, “such as food prepared in restaurants.” The federal budget deficit through 2031 would increase $54 billion, CBO says, as the government spent more on unemployment benefits and health-care programs.

Low-wage employees lucky enough to keep their jobs would get a raise. CBO says 17 million workers would be “directly affected” by the $15 minimum, and poverty “would be reduced by 0.9 million.” This is not a free lunch, no matter how often Mr. Biden and Bernie Sanders say so. Those gains would come at a high cost for the young and unskilled who will have a harder time grabbing the first rung of the economic ladder.

Even those figures are a guess, since setting the minimum wage at a high of $15 would essentially put the country through an economic experiment. This would mean imposing the urban labor costs of San Francisco and Manhattan on every out-of-the-way gas station in rural America. The U.S. economy is made up of local and regional labor markets with prevailing wage rates that depend on varying standards of living, the kinds of employers, and the availability and skill of the workforce. Some 20 states have a minimum wage no higher than the current national minimum of $7.25.

The good news is that the $15 wage’s route through Congress looks bumpy. Mr. Biden told CBS he’s willing to push a $15 wage floor in separate legislation, but he doesn’t think it’ll pass buried in his $1.9 trillion Covid bill: “Apparently that’s not going to occur because of the rules of the United States Senate.”

Mr. Biden is referring to the Byrd Rule. The Senate aims to approve his Covid bill using the budget reconciliation process, which bypasses a filibuster and requires only 51 votes. Under the Byrd Rule, however, the Senate parliamentarian should and probably will say a $15 minimum wage isn’t germane to the budget.

It won’t be for lack of trying. “We have a room full of lawyers,” Bernie Sanders said over the weekend, “working as hard as we can to make the case to the parliamentarian that, in fact, raising the minimum wage will have significant budget implications and, in fact, should be consistent with reconciliation rules.”

If the parliamentarian won’t bend, Democrats could hold a vote to overrule her. But in an interview last week with the Bipartisan Policy Center, Sen. Joe Manchin put his cards on the table. “I’m not going to let the Byrd rule be decimated,” he said. Can you blame him? West Virginia’s minimum wage is $8.75 an hour. Its median hourly wage, $16.31 in the 2019 data, is only a tick above what Mr. Sanders insists starting sandwich artists must be paid.