SACRAMENTO, Calif. — After a troubled rollout, President Barack 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 law’s benefits apply to individual policies as well as those offered through employers.

But one benefit didn’t take effect as expected after Supreme Court Justice Sonia Sotomayor late Tuesday night temporarily blocked the part of the law requiring some religious-affiliated organizations to provide their workers with insurance that includes birth control. Government officials have until Friday to respond to her emergency stay.

Administration officials said this week that 2.1 million consumers have enrolled through the federal and state-run health insurance exchanges that are a central feature of the Affordable Care Act. Millions more have been enrolled in Medicaid, after the federal law allowed states to expand the health insurance program for the poor.

Yet how many of those who signed up for 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 serious 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 rapidly, 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 still could bring plenty of confusion.

Insurers say they are receiving thousands of erroneous sign-up applications from the government, and some people who thought they had enrolled for coverage have not received confirmation. Undoubtedly, some will find out they don’t have the immediate coverage they thought they did.

Some states, including Minnesota and Rhode Island, extended their sign-up period until the final day of 2013, leading to a last-minute crush of paperwork for insurers. Call center wait times in Minnesota extended beyond two hours on Tuesday, a possible sign of heavy consumer interest.

Anticipating disruptions, major 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 independent pharmacies also are ready to help.

Some parts of the Affordable Care Act took effect previously, such as the ability of young people to remain on their parents’ insurance policies until age 26.

Others have been delayed until 2015, including the law’s requirement that companies with 50 or more workers must provide affordable coverage or pay fines. The administration says it’s trying to iron out burdensome reporting requirements.