All told, the Trump administration has reduced funds for the navigator program by 41 percent, to $36.9 million, from $62.9 million last year. Among the states hit the hardest, according to data provided to Congress by the administration, are Georgia, down 61 percent; Michigan, down 72 percent; New Jersey, down 62 percent; and Ohio, down 71 percent.

In the face of such numbers, some navigator groups have simply quit.

To Democrats and supporters of President Barack Obama’s signature domestic achievement, the cuts are another sign that President Trump will sabotage a law that he could not persuade Congress to repeal. To social workers in the trenches, eager to connect those in need with the insurance available, it is mystifying.

“When we received the notification, we were shocked, to say the least,” said Lisa Hamler-Fugitt, the executive director of the Ohio Association of Foodbanks, which was notified by the Trump administration that its budget would be cut by 71 percent, to $486,000, from $1.7 million. “We have yet to receive any explanation of the cut. We have met or exceeded every one of our performance metrics. There was never any feedback that gave us any indication that we were not going to receive the same amount.”

Indeed, in an email to the Ohio Association of Foodbanks earlier this year, the federal employee supervising its work, Donnamarie Spencer, said, “You guys are superstars!”

Her group decided to pull out of the navigator program altogether.

The cuts come at a time of turmoil in insurance markets, when more consumers than ever may need help navigating the health care system. Insurers are withdrawing from many markets, rates are shooting up more than 40 percent in some states and the enrollment season will be shorter than in the past. Mr. Trump has stoked uncertainty, saying he would “let Obamacare fail” and threatening to cut off certain subsidies paid to insurers for low-income people.