WASHINGTON — When Democrats passed President Barack Obama’s health care overhaul, they used Medicare cuts to pay much of the cost of providing insurance to millions of uninsured.

Now, lawmakers scrambling to stave off a scheduled 25 percent cut in doctors’ Medicare pay on Jan. 1 plan to reverse the flow. They’re tapping financing for the health care overhaul to keep Medicare from breaking down.

The $19 billion will help pay doctors at current rates for another year. It will come mostly from tightening the rules on tax credits in the health care law that make premiums more affordable, according to an agreement reached Tuesday by Senate leaders of both parties.

It might seem like the proverbial robbing Peter to pay Paul, with a game of budget tag thrown in.

As bewildering as it may seem, the maneuver shows how federal health care funding is increasingly connected — even among programs serving different constituencies. Just last week, Obama’s deficit commission called for a single government health care budget, a step to getting costs under control.

“Health care spending is a significant part of the federal budget,” said Alex Vachon, a health policy consultant who formerly served as a Senate GOP aide. “So if they are going to go looking for health care money, they’re going to want to get it from another health care program.”

The move also indicates there could be billions more to be squeezed from tweaks to the health care law.

Under the overhaul, millions of workers and their families will be eligible for tax credits to help them pay premiums. Those subsidies can add up to thousands of dollars per household in many cases. They’ll be available up front each year starting in 2014. The aid is based on income, and people who make less will receive more.

But what if somebody gets a raise, a bonus or a higher paying job later in the year — and they keep quiet about it?

If the government finds out, the law as originally passed said individuals would have to pay back up to $250, and families up to $400.

The latest deal would replace that formula with a sliding scale.