By RICARDO ALONSO-ZALDIVAR

WASHINGTON — President Barack Obama’s push to cover America’s uninsured faces another big test Monday.

This time, it’s not only how the website functions, but how well the program itself works for millions who are starting to count on it.

Midnight Monday, Pacific time is the deadline for new customers to pick a health plan that will take effect Jan. 1, and for current enrollees to make changes that could reduce premium increases ahead of the new year.

HealthCare.gov and state insurance websites are preparing for heavy online traffic before the deadline, which gives consumers in the East three hours into Tuesday to enroll.

Wait times at the federal call center started creeping up around the middle of last week, mainly due to a surge of current customers with questions about their coverage for next year. Many will face higher premiums, although they could ease the hit by shopping online for a better deal. Counselors reported hold times of 20 minutes or longer for the telephone help line.

About 6.7 million people now have coverage through Obama’s signature law, which offers subsidized private insurance. The administration wants to increase that to 9.1 million in 2015. To do that, the program will have to keep most of its current enrollees while signing up more than 2 million new paying customers.

People no longer can be turned down because of health problems, but picking insurance still is daunting for many consumers. They also have to navigate the process of applying for or updating federal subsidies, which can be complex for certain people, including immigrants. Many returning customers are contending with premium increases generally in the mid-to-high single digits, but much more in some cases.

Consumers “understand it’s complicated but they appreciate the ability to get health insurance,” said Elizabeth Colvin of Foundation Communities, an Austin, Texas, nonprofit that is helping sign up low-income residents. “People who haven’t gone through the process don’t understand how complicated it is.”

Last year’s open enrollment season turned into a race to salvage the reputation of the White House by fixing numerous technical bugs that crippled HealthCare.gov from its first day. With the website now working fairly well, sign-up season this year is a test of whether the program itself is practical for the people it is intended to serve.

New wrinkles have kept popping up, even with seemingly simple features of the Affordable Care Act.

For example, most current customers who do nothing will be automatically renewed Jan. 1 in the plan they now are in. At this point, it looks like that is what a majority intends to do.

While that may sound straightforward, it’s not.

By staying in their current plans, people can get locked into a premium increase and miss out on lower-priced plans for 2015. Not only that, they also will keep their 2014 subsidies, which may be less than what they legally would be entitled to for next year.

Doing nothing appears to be a particularly bad idea for people who turned 21 this year, according to the Center on Budget and Policy Priorities, a Washington group that advocates for low-income people.

Researchers at the center estimate that 21-year-olds will see a 58 percent increase in the sticker price for their premiums just because they’re a year older. An age-adjustment factor used to compute premiums jumps substantially when a person turns 21. A 20-year-old whose premium was $130 per month in 2014 will see the premium climb to $205 a month in 2015, solely because of that year’s difference.

Tax-credit subsidies can cancel out much or even all of the impact. But if consumers default to automatic renewal, their tax credits will not be updated and they will get the same subsidy as this year.

“Even in the best possible scenario of how many people we can expect to come in, we will still see a substantial number of people defaulting,” said Judy Solomon, a health care policy expert at the center. She worries that some young adults may get discouraged and drop out.

Reviews of HealthCare.gov and state health insurance exchanges are mixed.

An Associated Press-GfK poll this month found that 11 percent of Americans said they or someone else in their household tried to sign up since open enrollment began Nov. 15. Overall, 9 percent said the insurance markets are working extremely well or very well. Twenty-six percent said the exchanges are working somewhat well, and 39 percent said they were not working well. The remaining 24 percent said they didn’t know enough to rate performance.

So far it has been a frustrating experience for Marie Bagot, of Fort Lauderdale, Florida. She and her husband are in their 60s, but not yet old enough for Medicare. The husband, who works as a chef, will turn 65 around the middle of next year and qualify for Medicare. Bagot said they were happy with their insurance this year under Obama’s law.

“As you get older, you worry about your health,” she said. “I was very pleased with the price we got.”

But Bagot said she received a notice from her insurer that her current plan will not be available next year in her community. The closest alternative would involve a premium increase of more than $350 a month, even with their tax credit subsidy. After days of trying to find a comparable plan through the federal call center and after visiting a counselor, Bagot said she opted to keep their current coverage, while hoping costs go down after her husband joins Medicare.

“I cannot afford it, but I’m going to try to,” she said.

Monday is not the last chance for consumers like Bagot. Open enrollment doesn’t end until Feb. 15.