“All the finger pointing has overshadowed the discussion about the actual substance of the budget deal,” said Maya MacGuineas, president of the Committee for a Responsible Federal Budget, “and many lawmakers don’t even seem to care that the deal they are considering — which will almost certainly include even more tax cuts following the unaffordable tax bill Congress just passed, as well as new spending increases — will add tens of billions to the deficit. There is almost zero discussion of the ongoing damage on the nation’s finances.”

The health care taxes were all created as part of the Affordable Care Act, where they were designed to offset the cost of expanding insurance coverage to low- and middle-income Americans. But many of them, such as a tax on medical devices, have remained unpopular, and their implementation has been suspended or postponed before.

Those delays have been preferable to lawmakers than eliminating the taxes entirely, given a total repeal would have added an estimated $310 billion to federal budget deficits over the next decade, Ms. MacGuineas’s organization calculates. That price tag was too high to be included in the 2017 tax bill, which was limited in scope by Republicans’ decision to pass the bill on party lines using a budget reconciliation bill that only allowed for $1.5 trillion in revenue losses over a decade.

The bill to end the shutdown, which funds government operations through Feb. 8 and also includes a six-year reauthorization of the Children’s Health Insurance Program, did not move through budget reconciliation, the parliamentary procedure that circumvents filibusters in the Senate. That allowed Republican leaders to include the delays in the health insurance taxes without worrying about their fiscal cost, a move that drew few objections from Democrats.

All three health care taxes have been extensively discussed and debated by Congress since the passage of the Affordable Care Act.