The proposal is politically problematic for President Obama, however, since it is similar to one he denounced in the presidential campaign as “the largest middle-class tax increase in history.” Most Americans with insurance get it from their employers, and taxing workers for the benefit is opposed by union leaders and some businesses.

In television advertisements last fall, Mr. Obama criticized his Republican rival for the presidency, Senator John McCain of Arizona, for proposing to tax all employer-provided health benefits. The benefits have long been tax-free, regardless of how generous they are or how much an employee earns. The advertisements did not point out that Mr. McCain, in exchange, wanted to give all families a tax credit to subsidize the purchase of coverage.