The 2015 filing season could be the most difficult in decades, officials said. Ms. Olson said new paperwork resulting from the Affordable Care Act would probably exacerbate problems with customer service, which “has reached unacceptably low levels and is getting worse.”

“The I.R.S. is unlikely to answer even half the telephone calls it receives,” she added. “Taxpayers who manage to get through are expected to wait on hold for 30 minutes on average and considerably longer at peak times.”

Timothy S. Jost, an expert on health law at the Washington and Lee University School of Law who supports the Affordable Care Act, said: “It will be very easy to find people who are unhappy with the new tax obligations — people who have to pay a penalty, who have to wait forever to get through to somebody at the I.R.S. or have to pay back a lot of money because of overpayments of premium tax credits.”

Taxpayers normally report income and compute taxes annually. But the health care law is different. Consumers may be subject to tax penalties for any month in which they had neither insurance coverage nor an exemption.

The calculations will be relatively simple if all members of a household had coverage for every month of 2014. They can simply check a box on their tax return. But lower-income people often have changes in employment, income and insurance. If any members of a household were uninsured in 2014, they must fill out a work sheet showing coverage month by month, and they may owe penalties.

To claim tax credits, consumers need to fill out I.R.S. Form 8962, which includes a matrix with 12 rows and six columns — a total of 72 boxes, to compute subsidies for each month. Most taxpayers use software to prepare returns, and that will simplify the process, officials said.

Federal officials have authorized more than 30 types of exemptions from the penalty for not having insurance. One is for low-income people who live in states that did not expand Medicaid. Another is available to people who would have to pay premiums amounting to more than 8 percent of their household income. The government will also allow a variety of hardship exemptions and in most cases will require taxpayers to send in documents as evidence of hardship.