But some health care experts and economists said that an expanded use of the health system might start to have the opposite effect. Americans feeling more economically confident might demand more procedures from doctors and hospitals. Insurers paying more money for those procedures might, in time, increase premiums, cutting into wage gains. The government might end up spending more on the health law than current projections imply.

“We knew this was coming,” said Douglas Holtz-Eakin, a former head of the Congressional Budget Office and a prominent Republican economist, of rising spending because of the coverage expansion and improving economy. “The question now is whether we can hold spending down.”

Many other analysts said they had long expected health spending to increase. “If we are seeing an uptick, it’s the beginning of the uptick,” said Drew Altman, the president of the Henry J. Kaiser Family Foundation. “We’ve expected to see a lagged effect, both when the economy declines and when it improves.”