MIAMI » After two months of false starts, error messages and pleas for patience from the once-hobbled federal online health care exchange, Karen Egozi, the chief executive of the Epilepsy Foundation of Florida, watched Monday as counselors navigated the website’s pages with relative ease.

Click. Next page. Click. Next page. The website was working so well that Egozi, who oversees the 45 navigators in eight locations who help consumers enroll in health plans, said her team gave the system an 8 on a scale of 1 to 10, meaning that most people got as far as selecting a plan or taking home information to select a plan. It felt like a champagne moment.

"I’m 80 percent satisfied," Egozi said. "I think it will be great when it’s 100 percent."

A little over a week after the deadline that President Barack Obama gave for fixing the federal health care exchange, the system is definitely working better, according to consumers and navigators interviewed in several states. The technical errors that had bedeviled visitors to the site for weeks seemed to have been tamed by the patchwork of hardware and software fixes ordered by the administration, and applicants were finally selecting health care plans under the president’s new law, the Affordable Care Act. By last week, the number of applicants who dropped a plan into their virtual grocery carts was climbing at a rapid clip.

Still, the interviews indicated, some technical obstacles persist. After shoppers clicked all the way to the plans, for example, the system was not letting some people choose one. In other cases, people were asked to try again later.

Improved entry into the online marketplace has also exposed a new layer of problems and confusion for applicants who are suddenly finding their efforts to buy insurance delayed by requirements that they provide proof of identity or citizenship or that they wait for determinations on Medicaid eligibility.

For the most part, though, the news for the beleaguered online exchange, which serves 36 states, is improving. Since early December, the federal exchange website has run without crashing, officials said. In the first five days of December, about 112,000 people selected plans – compared with about 100,000 in all of November and only 27,000 in October. Last week, more than half a million people created accounts on the federal website, according to people familiar with the health care project.

Technical experts involved with the exchange said they are now preparing for a surge of applications before Dec. 23, the enrollment deadline to receive coverage by the first of the year. Although those preparations will require some significant changes to the system, the work will be easier now that the site seems stable during heavy use, the experts said.

In offices spread across the country, from Florida and Pennsylvania to Wyoming and Wisconsin, all of them states that rely on the federal government’s insurance exchange, navigators and applicants reported far fewer problems.

"I was hearing so much about the glitches in the system that I was worried that it wouldn’t work," said Caroline Moseley, 54, who lost her job as a housing program analyst for the city of Philadelphia. After asking a navigator from the nonprofit Resources for Human Development for help in finding a plan, Moseley chose one that costs $27 a month with a $6,000 deductible. "It was a great experience," she said. "The site was running very smoothly. It took about 30 minutes, tops."

Stephanie Lincoln, 60, of Lansdowne, Pa., also had quick success with the exchange — after a frustrating experience trying to submit an application online in October and November. With the help of a navigator, Caroline Picher, working at the local library, Lincoln signed up in just one hour on Friday for a policy that will cost $113 a month, with no deductible.

"I am one of the people whose plans were canceled," Lincoln said. "It was just the easiest thing in the world."

But the smoother functioning of the website has also brought to light new kinds of delays that are creating anxieties for some of the people rushing to buy insurance by the Dec. 23 deadline.

At Wyoming Senior Citizens in Riverton, Wyo., four people walked in Thursday and Friday and completed their applications with the help of counselors. After they entered their personal information, the system displayed a message saying they needed to check if they qualified for Medicaid, said Karla Borders, a navigator at the center.

Borders said the clients already knew that they did not qualify because they had applied before and been denied. But the website would not allow them to proceed with their enrollment, informing them that they would be notified if they were indeed eligible for Medicaid, which can take a week. "Now they’re basically being put back in the system," Borders said. "It just kind of puts them in limbo until they get another denial letter."

In general, health policy experts said, people must be checked for eligibility for Medicaid before they can get tax credits to help pay premiums for health insurance purchased on an exchange. Under the 2010 health care law, people generally cannot receive tax credits if they are eligible for "minimum essential coverage" from other sources like Medicaid and Medicare.

Asked about the problems reported by consumers and insurance counselors, Aaron Albright, a spokesman at the federal Centers for Medicare and Medicaid Services, said: "HealthCare.gov is working smoothly for the vast majority of users. We’ve acknowledged that there are some consumers who may be better served through in-person assistance or call centers. There will be some people who have technical difficulties or complicated family or tax situations that will be better served through other pathways."

In West Palm Beach, Fla., John Foley, a lawyer and certified counselor for the Legal Aid Society of Palm Beach County, said now that applicants are moving beyond the initial application stages, he and others in Florida have hit upon another problem that could delay enrollment for some: Naturalized citizens are being asked by the system for a citizenship number that appears on their naturalization documents.

U.S. passports, which require proof of citizenship, are not allowed as substitutes. Foley said some of his clients, particularly those who were naturalized long ago, have misplaced that document or don’t know where it is. A copy costs more than $300, a prohibitive amount for some people.

"Some people go home and they hunt and it takes them a week to find the document," Foley said. Despite such problems, many enrollment counselors said, they have been deluged with phone calls and walk-ins.

Linda Lott at the Jessie Trice Community Health Center in Miami said her office was feeling more confident that appointments with clients might actually yield enrollment these days. And while some people remain puzzled about the process, wondering why, for instance, they must wait to be billed by insurers instead of being able to pay for their insurance online a la Amazon, things were significantly better.

"I’m feeling very good about it," Lott said. "We’re enrolling people."

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Lizette Alvarez and Jennifer Preston, New York Times