But be prepared to hit redial. John Koskinen, the Internal Revenue Service commissioner, admitted in a recent speech that because of budget constraints, the agency may be equipped to answer just over half of the phone calls it receives. Many will get a “courtesy disconnect.”

The tax filing season will also serve as yet another big test for the federal government, since it will require several government entities — the state and federal marketplaces and the I.R.S. among them — to share data and send out new tax forms with accurate information in a timely manner.

Here are some of the biggest ways the new law may affect taxpayers:

EXEMPTIONS Consumer advocates said they were concerned that some taxpayers might not realize that they needed to apply for certain exemptions, and, in some cases, substantiate their circumstances. (An estimated 23 million people will qualify for an exemption in 2016, while many others will be granted a pass because of a hardship, according to a federal analysis.)

Some exemptions must be applied for through the exchanges, while others can be claimed only on income tax returns and some can be granted through either channel. (The I.R.S. and Healthcare.gov have lists of where to apply for each). For instance, people who cannot find affordable coverage — costing 8 percent of household income or less — must claim that exemption on their tax returns.

But the most time-consuming exemptions require mailing a signed paper application to the exchanges: These are processed manually, which can take a couple of weeks. Those exemptions include several hardships, such as foreclosure, the death of a family member, unpaid medical bills and eviction, as well as religious reasons for not using insurance. “Do it now because it’s a cumbersome process,” advised Mark Steber, chief tax officer at Jackson Hewitt Tax Service.