SACRAMENTO, Calif. — After a troubled rollout, President Obama’s health care overhaul now faces its most personal test: How will it work as people seek care under its new mandates?

Most major pieces of the Affordable Care Act take full effect with the new year. That means people who had been denied coverage because of a pre-existing medical condition can book appointments and get prescriptions.

Caps on yearly out-of-pocket medical expenses will mean people shouldn’t have to worry about bankruptcy after treatment for a catastrophic illness or injury. And all new insurance policies must offer a minimum level of essential benefits, ranging from emergency room treatment to maternity care.

The benefits apply to individual policies as well as those offered through employers.

The burden for implementing the law now shifts to insurance companies and health care providers.

Dr. John Venetos, a Chicago gastroenterologist, said there is “tremendous uncertainty and anxiety” among patients who have been calling his office, some of whom believe they have signed up for coverage but have not received insurance cards.

“They’re not sure if they have coverage. It puts the heavy work on the physician,” Venetos said. “At some point, every practice is going to make a decision about how long can they continue to see these patients for free if they are not getting paid.”

Administration officials said this week that 2.1 million consumers have enrolled through the federal and state-run insurance exchanges that are a central feature of the Affordable Care Act.

Yet how many of those who signed up for health coverage on the exchanges will follow through and pay their premiums will not be known for a couple of weeks. People who signed up on the federal website have until Jan. 10 to pay premiums for coverage retroactive to Jan. 1, while consumers in some states have until Jan. 6.

Those who enrolled during the exchanges’ first three months, persisting through technological problems and jammed call center phone lines, are probably motivated to make sure they have a policy in place as soon as possible, said Anthony Wright, executive director of Health Access California, which advocates for lower-income people and supports the federal health care changes.

“These are people who made a point of signing up and signing up before the deadline so they could start on Jan. 1. That suggests to me that that will be a population that is more likely to follow through with the payment,” he said.

Premiums paid after the deadline will be applied to coverage starting Feb. 1 or later. Consumers have until March 31 to sign up in time to avoid a federal tax penalty for remaining uninsured. That fine starts at $95 for an individual this year but climbs to a minimum of $695 by 2016. There is an additional fine for parents who do not get health insurance for their children.

Although the federal website is apparently fixed for consumers, the start of the year was expected to bring plenty of confusion.

Medicaid, the state-federal health insurance program for the poor, already was experiencing problems in some states.

Even before the January start of coverage, health insurance companies said they were receiving thousands of erroneous sign-up applications from the government, and some people who thought they had enrolled for coverage have not received confirmation. Some states extended their sign-up period until the final day of 2013, leading to a last-minute crush of paperwork for insurers.

Anticipating disruptions, drug store chains such as CVS and Walgreens have announced they will help customers who face coverage questions, even providing temporary supplies of medications without insisting on up-front payment. Many smaller pharmacies also are ready to help.