PHOENIX » Steven Norton, recovering from a severe stroke, is renewing the health plan he got this year through the Affordable Care Act insurance exchange. He will pay more in 2015 — $501 a month including his federal subsidy, up from $485. But for him, continuity matters more than price, so he has not logged on to HealthCare.gov to search for alternatives.

"If it’s working, why try to fix it?" Norton, 51, said.

Nancy Allman, a retiree outside Tucson, sees things differently. Allman, 64, was surprised to learn her exchange plan would cost $235 a month next year after her subsidy, up from $158. Overwhelmed by her choices on HealthCare.gov, she called the customer service line and received help finding a plan from a different insurer that will cost only $77 a month. The plan has a smaller network of providers, but it includes her primary care doctor, and she is in good health.

"It was like a no-brainer to switch," she said.

Across the nation, millions of people who bought insurance through the exchange in this inaugural year of coverage under the health care law must decide by Monday whether to switch plans for 2015 if they want a new plan starting Jan. 1. If they do nothing, most of the 6.7 million people who remained enrolled as of last month will automatically be re-enrolled in their current plans or similar ones. More often than not, those in the most popular plans will see their premiums increase, according to a New York Times analysis of data from the McKinsey Center for U.S. Health System Reform.

The Obama administration is urging them to shop around, and with good reason: Many can find a better deal or at least keep their costs steady. That is especially true in states like Arizona, where the competition is robust, new insurers have entered the marketplace and the price for the cheapest plans in many areas has dropped.

At the same time, the availability of cheaper "benchmark" plans means that the federal subsidies that help many lower-income Arizonans pay their premiums will go down, because subsidies are pegged to those plans. That means customers who stay in more expensive plans will have to pay a larger share of the price.

Another potential problem is that subsidy recipients will get the same amount in 2015 as they did in 2014 unless they ask for a recalculation. That means some people could be required to pay back part of their subsidy at tax time.

Despite those issues, the data so far suggests that many HealthCare.gov customers are keeping what they have and not even window-shopping. As of Dec. 5, only about 720,000 customers had returned to the federal exchange serving 37 states to re-enroll or switch plans, according to the Department of Health and Human Services.

Here in Arizona, insurance agents and enrollment counselors last week reported a steady stream of customers seeking advice. But the demand has not yet been huge, they said, indicating that many enrollees may be succumbing to inertia, are willing to pay more to their keep their networks and level of coverage, or are unaware that they have a choice. About 120,000 residents of Arizona signed up for exchange plans this year, according to federal data.

"I’m concerned about the confused," said Kathleen Oestreich, chief executive of Meritus, a new insurer, which, after dropping its rates by 23 percent on average, is offering many of the lower-priced plans here for 2015. "That natural inclination to simply not change because it’s too much effort: How will it affect the population of low-income people in particular?"

Shanna Goldenberg of Phoenix, who works two jobs and pays $160 a month for her exchange plan, said she had no idea if her premium was going up. But Goldenberg, 27, said she would probably let her plan be automatically renewed, because the enrollment process last year was so confusing.

"I’m the kind of girl who just sticks with what’s easy," she said in an email.

But in a later note, Goldenberg said she had discovered her plan would not be offered next year, adding: "I guess now I have to shop around again. … If only I can figure it out this time."

Norton did call HealthCare.gov on Thursday for a recalculation of his subsidy. It will drop by $30, he learned, and his portion of the premium will grow to $385 from $338.

Oestreich said those who were researching their options seemed fairly savvy about insurance. That is a big change from last year, she said, when many HealthCare.gov customers seemed baffled by the enrollment process and the policies they were buying.

"They are calling with specific questions and looking for specific products," she said. "In many cases, they’re buying up a little bit — going to a little bit bigger network because they’ve understood the value of that."

In other states, too, enrollment groups said that people shopping around were asking smart questions.

Brenda Cardenas, an enrollment counselor in Phoenix who helped dozens of families sign up for coverage last year, said that only about 15 had sought her help with the renewal process as of last week. Most people are picking new plans, often ones with smaller networks of doctors and hospitals, to avoid paying more, she said. For many, the switch will require finding new doctors, but Cardenas said nobody had complained so far.

"For a lot of our consumers, this is the first year they’ve had health coverage," she said. "For them, switching to a new provider isn’t a big deal yet."

In one case, Cardenas said, a couple learned the amount of their subsidy would drop by $66 because of the availability of new lower-cost plans that influence the calculation. They decided to switch from a Health Net plan with a large network of providers and no deductible to a Meritus plan with a smaller network and a $1,000 deductible. By doing so, she said, they will spend almost $200 less per month.

Health Net signed up 65 percent of exchange enrollees here this year, but its rates are rising by an average of 12 percent, a company spokeswoman said. Altogether, 11 insurers are selling on the exchange here for 2015, up from eight.

Leslie McGee, an acupuncturist in Tucson, also found a better deal when she went to HealthCare.gov and updated her personal information. Her income has dropped, so she will qualify for a subsidy in 2015 after receiving none this year. The premium on her current plan is increasing by 17 percent, so she is switching to a different insurer and will save $100 per month.

McGee, 60, will have higher out-of-pocket costs if she goes to the doctor, but she is gambling that she will need only preventive care, which is free.

"I am very grateful," she said of the new price. "I wasn’t surprised with my rate increase, but I also wasn’t willing to go there."

Michelle Steinberg, 54, of Phoenix, is avoiding a 23 percent increase by switching to a cheaper plan that will not cover as much of her medical costs. Her premiums will still increase 13 percent, to $450 a month, but she said she was satisfied with her new choice, which has a lower deductible.

"I’m not averse to switching companies," said Steinberg, who is moving from Health Net to United Healthcare.

The big question is whether people who have not yet shopped around will flock to the online exchanges by Monday in a last-minute crush — and whether those who do not will later regret it. They can switch until Feb. 15, when open enrollment ends, but their new coverage will not begin until February or March if they wait past Monday.

In Maitland, Fla., Rebecca Pando, 60, said that she was happy to do the painstaking research to find a new plan.

Her insurer, Florida Blue, is replacing her plan with one that has a substantially higher deductible: $5,000 compared with $1,300. Pando found a new plan from United Healthcare that will cost $400 a month in premiums, about $50 less than what she paid this year including her subsidy. It has a $4,000 deductible, she said, but a better choice of doctors.

"It’s pretty time-consuming and you get a little crazy," Pando said of the shop-and-compare process. "But it certainly is better than not being able to buy insurance."

© 2014 The New York Times Company