As the Obama administration closes in on its self-imposed deadline to fix the troubled online health insurance marketplace, consumer advocates say it is becoming easier for people to sign up for coverage but insurers warn that critical flaws continue to hinder participating health plans.

Administration officials have promised that will be working smoothly for most people by Saturday and are citing evidence indicating progress toward that goal. Workers helping people sign up for coverage have noticed that the site has been running better over the past two weeks, with consumers experiencing shorter wait times and fewer crashes.

But the online system is still marred by defects that will create havoc for insurance companies if a significantly larger volume of applicants starts to sign up in coming weeks. Among them are the error-riddled reports that insurers are receiving about who has enrolled, a problem that could be disastrous if not fixed soon.

There is little room for error at this point. People seeking to take advantage of the new coverage that kicks in Jan. 1, or whose health insurance policies are being canceled at the end of the year, have until Dec. 23 to choose a plan and until Dec. 31 to pay their first month’s premium. Some congressional Democrats, uneasy about the messy rollout of the exchange, have expressed a willingness to dismantle parts of the law if problems continue.

“If they get this fixed, it’s a chapter in somebody’s book. If they don’t get this fixed, it’s a chapter in history,” said Michael O. Leavitt (R), a former Utah governor who served as secretary of the Department of Health and Human Services during the tumultuous rollout of Medicare Part D, which added prescription drug coverage to Medicare. “They will need to demonstrate fairly soon that there’s improvement, or they will lose the support of their own party.”

On Friday, Sen. Al Franken (D-Minn.) told Minnesota Public Radio that if the Web site isn’t fixed on time, he would consider delaying the rule requiring most Americans to carry health insurance or face a fine. He joins a growing chorus of Democrats in Congress who have advocated for changes or delays to the law that could weaken it.

Administration officials contend that they are on track. By Saturday, they said, they will have doubled capacity to allow at least 50,000 users at a time without the system malfunctioning. They are also working on a new system that gives people alternate ways to sign up for coverage and get government subsidies, including going directly to insurers’ corporate Web sites.

They are also moving on to the outreach phase, which had taken a back seat as they grappled with the faulty Web site. Next week, the White House will host an insurance-oriented “youth summit” aimed at people ages 18 to 35, an age group whose participation in the health-care law will be critical to its success.

On Tuesday, White House officials are scheduled to meet with physicians, nurses and pharmacists about the health-care law.

Administration officials have sought to tamp down expectations, noting that improvements will be gradual in the coming weeks and months.

“The system will not work perfectly on Dec. 1, but it will operate much better than it did in October,” Julie Bataille, a spokeswoman for the Centers for Medicare & Medicaid Services, the federal agency in charge of, told reporters on Monday.

Even if it does work better for consumers, there are still problems — particularly the scrambled reports insurers are getting about people who have signed up for coverage through Insurers say they are getting duplicate records and reports that misstate family relationships, such as listing a child as a spouse.

In some cases, enrollment reports are disappearing. With these “orphan records,” insurers have no way of knowing whether a person is signed up for coverage, unless a new customer happens to call the company with questions.

“The biggest concern is that there are going to be people showing up to get their care,” said one person close to the insurance industry, who spoke on the condition of anonymity to discuss sensitive issues. “Then [the doctors or hospitals] call us and we have no record, and then the consumer is left frustrated and worried and scared.”

Until such errors stop, “you can’t open the floodgates” to large numbers of Americans using the Web site to sign up for coverage, said an insurance industry official who also spoke on the condition of anonymity to discuss private conversations with administration officials about how to improve the system.

The ripple effects of these flaws affect consumers, because the new coverage does not begin until they pay their first monthly insurance premiums. And without accurate information about new customers, health plans cannot send them correct bills.

Beyond the troubles with enrollment forms, which have been evident since the marketplace opened on Oct. 1, insurers are anticipating problems if IT workers from the government and outside contractors cannot soon build other parts of the online system that are running behind schedule.

For instance, starting in mid-December, the government and each participating insurance company are supposed to perform a monthly “reconciliation,” to make sure that each side has the same list of new customers, the benefits chosen by the consumers and the government subsidies for which they qualify. That feature of the online system, however, has not been built, according to people close to the industry and government officials.

Nor can the system handle another feature, scheduled to be ready when health plans take effect on Jan. 1, in which insurers are to be paid extra government money, through a method known as “risk corridors,” if their new customers are old and require expensive medical care. “It’s not built, let alone tested,” the industry official said.

Still, consumer advocates report steady improvement in since its launch. For example, about half of the people at a Nov. 7 Miami-Dade Community College enrollment fair in Florida were able to create accounts and peruse their options, said Justin Nisly, a spokesman for the advocacy group Enroll America. By the second fair on Nov. 16, that proportion had risen to 2 out of 3 people.

The news is heartening enough that Enroll America is going forward with its “chase” campaign Dec. 1 — following up with 50,000 uninsured people in 10 states to say, “If folks have had a frustrating experience on the Web site . . . why don’t you go back and try again,” Nisly said.