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To pay for the credits, the plan would change what aides said was a “distortion” in the tax code that excluded all of a person’s employer-sponsored health care coverage from taxation. Instead, it would cap the exclusion at 65 percent.

Aides said the change should put downward pressure on premiums. They argued that the full exclusion artificially inflated the rates of increases in health insurance premiums.

Ben Wolfgang contributed to this report.