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But Mr. Barrasso said there “would be an outcry” if Mr. Obama cut a deal to accommodate unions.

Republicans say the White House favored big business over everyday folks when it decided to delay, until 2015, a mandate requiring employers with 50 or more full-time workers to provide coverage. But the administration did not delay the individual mandate requiring most Americans to obtain some form of insurance.

For days, Republican critics of the law have seized upon the particularly harsh language that Teamsters boss James Hoffa and two other leaders — Joseph Hansen, president of the United Food and Commercial Workers, and Donald “D” Taylor, president of United Here — used in their letter to Democratic leaders.

Senate Minority Leader Mitch McConnell, Kentucky Republican, said “when even cheerleaders for the law start to become its critics, that’s when you know there’s something to this ‘train wreck’ thing everyone keeps talking about.”

The unions cited Mr. Obama’s promise that if Americans liked their health care plans, they would be able to keep them.

“Sadly, that promise is under threat,” the unions wrote, saying they would withdraw their support unless their grievances are rectified.

“This is especially stinging because other stakeholders have repeatedly received successful interpretations for their respective grievances,” they wrote, citing the decision to delay the employer mandate after business owners complained about its complex reporting requirements.

The Republican-led House voted last week to codify the White House’s one-year delay of the employer mandate, with 35 Democrats supporting the measure. Nearly two dozen Democrats also voted to delay the individual mandate.

The bill is unlikely to gain traction because supporters of the health care act say the mandate is needed for the law to be effective.

In the meantime, Sen. Orrin G. Hatch, Utah Republican, is trying to team up with unions to “permanently delay” the health care reforms.

“I hope,” Mr. Hatch told the unions in a letter, “you will accept my invitation to provide relief from the law to all Americans and ensure that the law will no longer threaten access to insurance, increase costs, or deny individuals from keeping their existing health insurance plans as the president had promised.”