Their negotiations produced changes to a tax included in the bill passed by the Senate last month. The changes would lessen and delay the impact of the tax on workers and would reduce the amount of revenue collected. The revenue would help finance coverage for millions of people who are uninsured.
Labor leaders hailed the deal and said they were prepared to fight for passage of the legislation.
“We have seen tremendous progress over the last couple of days,” said Richard L. Trumka, president of the A.F.L.-C.I.O.
Under the bill passed last month by the Senate, the federal government would have imposed a 40 percent tax on the value of employer-sponsored health coverage exceeding $8,500 a year for an individual and $23,000 for a family. The tax would have taken effect in 2013. White House officials, Democratic Congressional leaders and labor unions said Thursday that they had agreed to an increase in those thresholds to $8,900 for an individual and $24,000 for a family. Moreover, they said, starting in 2015, the cost of separate coverage for dental and vision care would be excluded from the calculations.
In addition, they said, health plans covering state and local government employees and collectively bargained health plans would be exempt from the tax until 2018. This transition period addresses the concerns of schoolteachers and other public employees who have denounced the tax.
For people in certain high-risk occupations, including police officers and construction workers, thresholds would be higher: as high as $27,000 for a family.
In addition, Mr. Trumka, who led a team of labor leaders negotiating with the White House, said the thresholds would be increased for “age and gender,” to reflect the higher premiums often charged for health plans with large numbers of women, older workers and retirees.
He said the changes would reduce the amount of revenue from the tax by about 40 percent, to $90 billion over 10 years. The tax in the Senate bill would have generated $149 billion over 10 years.
A White House official, speaking to journalists on condition of anonymity, said he did not know how much revenue would be lost as a result of the changes. The White House said that the tax would still tend to slow the growth of health spending, and that the overall bill would not add to the federal budget deficit.
President Obama and Congress will find ways to offset the loss of revenue from the tax, the White House said.
Republicans said the agreement was another special deal to win votes for the legislation by mollifying some of the Democrats’ most loyal supporters.
Progress in the negotiations came as Mr. Obama addressed House Democrats on Capitol Hill. He exhorted them to finish the job on health care despite fierce criticism from Republicans and fears among some Democrats that they could pay a political price for passing the legislation.
“Let me tell you something,” Mr. Obama said, pointing to elements of the legislation he said would increase access to health care. “If Republicans want to campaign against what we’ve done by standing up for the status quo and for insurance companies over American families and businesses, that is a fight I want to have.”
The agreement has not been vetted by rank-and-file members of the Democratic caucus in either house of Congress. Nor has the Congressional Budget Office reviewed it. The proposed tax could be further modified based on feedback from lawmakers and the budget office.
Mr. Obama and some economists contend that the tax could help rein in health spending by encouraging employers to reconfigure health benefits.
While insurers would be responsible for paying the tax, the Congressional Budget Office and private economists say the cost would be passed on to workers and retirees.
Representative Joe Courtney, Democrat of Connecticut, who has led opposition to the tax, said the agreement indicated that “a lot more intelligence is being applied to this issue.” But he added: “I am reserving judgment. I would like to see more detail.”
The tax could affect a significant number of health plans in the future because the thresholds would probably rise less than health costs and insurance premiums. Under the deal, as in the Senate bill, the thresholds would rise with the Consumer Price Index, plus one percentage point.
The thresholds would be further increased if insurance costs grow faster than expected from 2010 to 2013.
Gerald W. McEntee, president of the American Federation of State, County and Municipal Employees, said he spoke to members of the House Democratic Caucus at their conclave on Thursday.
“They were quite receptive, although there were some people who wanted to fight for no excise tax at all,” Mr. McEntee said.
Republicans said the special treatment of collectively bargained health plans was a favor to union members, who have supported Democrats with campaign contributions and votes.
Representative John Kline of Minnesota, the senior Republican on the House Education and Labor Committee, said that while union members might avoid the tax on high-cost health plans for five years, nonunion workers would have to pay it.
“This latest back-room maneuver is another example of how administration officials and their enablers in Congress will cut deals with their special-interest allies to impose a government takeover of health care,” Mr. Kline said.
White House officials defended the provision, saying it would allow employers, employees and insurance companies to prepare for the new tax.
Under the agreement, Mr. Trumka and White House officials said, people in collectively bargained health plans could buy coverage through new government-regulated markets, known as insurance exchanges, starting in 2017. The officials said they were still working with Congress on details of this arrangement.