Conservatives, of course, have bashed the Affordable Care Act since before it was passed in 2010, and aspects of the legislation remain unpopular across the country.

Ahead of the opening on Oct. 1 of the health insurance marketplaces created to cover the uninsured by the law, the president is facing rising anger from some of the most loyal members of his party base. Compounding the unions’ anger, the business community — often labor’s archenemy and a frequent Obama critic on health care — received an important reprieve this summer when the administration delayed for one year the requirement that employers offer their workers’ health coverage or face a penalty of $2,000 for each uninsured full-time employee.

“Our members are the exact type of people that Obamacare was supposed to take care of,” said D. Taylor, president of Unite Here, a union of hotel and restaurant workers that has about 200,000 members with Taft-Hartley plans, employer-provided coverage named after the 1947 labor law. “We were the first union to endorse Obama. We were big supporters of health care reform.”

Mr. Taylor cast doubt on the president’s assurances that those Americans who liked their health plans could keep them.

“Under the way the A.C.A. has been rolled out by the Treasury and I.R.S. regulations, it will make it completely impossible to live up to that,” he said. “We think this is an example of unintended consequences. And it’s completely disheartening that the biggest earlier supporter of the president hasn’t gotten the same listening and benefit of big business with the one-year delay in the $2,000 penalty.”

Labor’s dismay is not new, but union leaders had been restrained, waiting for their closed-door negotiations with the administration on this issue to bear fruit. That anger burst into the open this summer when the so-called employer mandate was postponed.

Some state labor federations have passed resolutions excoriating the health law. Mr. Trumka, torn between trying not to anger the administration while mollifying some of his unions, may have headed off a full-throated call to repeal the law entirely, but some union presidents say they believe they have no other choice.