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But even the proposal sitting before the Senate, which taxes these “Cadillac plans” less than the bill signed into law, expects to raise $32 billion during the 2018-19 period. The “fix” heavily penalizes health-insurance plans costing more than $10,200 for individuals and $27,500 for families — imposing a 40 percent excise tax on the value above those amounts.

Many of these “Cadillac plans” are held by union workers in the private sector and by state and local government workers. Most families of both groups earn well below $250,000.

While the excise tax will be directly paid by the insurance company, economists of all persuasions expect the costs to be passed along to policyholders.

Middle- and working-class Americans, Republicans say, also can expect to pay a big portion of the numerous fees that the health care bill will impose on the pharmaceutical industry ($27 billion from 2011 through 2019), on medical-device manufacturers ($20 billion from 2013 through 2019) and on health insurance providers ($60.1 billion from 2014 through 2019), and on indoor tanning services (a 10 percent excise tax).

The new law also limits deductions for medical care, requiring people, including middle-income households and seniors, to have spent more of their own money on health care expenses before they become tax-deductible. Currently, expenses above 7.5 percent of adjusted gross income can be deducted for tax purposes; the bill Mr. Obama signed raises that threshold to 10 percent of income.

The legislation imposes mandates on employers with more than 50 workers to provide health insurance to their workers and on individuals and families to carry health insurance. The bill would impose penalties on those employers ($52 billion from 2014 through 2019) and households ($17 billion from 2014 through 2019) who do not comply with the mandates.

In part because these penalties would be administered and enforced by the Internal Revenue Service, Republicans consider them taxes and violations of Mr. Obama’s campaign pledge.

The White House declined to respond to a request for comment on the charge that the president broke his promise not to raise taxes on middle-income households.