D.C. lawmakers on Thursday congratulated themselves for a health exchange running far more smoothly than that in neighboring Maryland even as health-care brokers said problems remain and some District residents have been mired in the process of selecting insurance plans for six weeks or more.

The testimony before the D.C. Council’s Health Committee offered the first look inside the health-care exchange since October. Mila Kofman, the exchange’s executive director, said it has enrolled 20,290 people — about 37 percent of whom are young adults, compared with 24 percent nationally.

“We know we are reaching those people who are uninsured and . . . achieving our goal of having a mix of younger and older people,” Kofman said. “But we know that not everyone has had the same experience. . . . We remain very committed to improving the user experience.”

Kofman said the city’s site, known as DC Health Link, was bombarded “millions of times” by cyberattacks during its Oct. 1 launch. The firewall held and no enrollees’ data were compromised, she said, adding that a review of the attacks found that many were launched overseas.

Health-care brokers who help D.C. residents navigate the site warned that naturalized citizens, those with thin credit records and those with complicated family arrangements can easily get tripped up in the automated, online application process.

“My experience has been absolutely futile. I have not been able to complete one application,” said Sandra Address, the owner of a small health-care brokerage who has been trying to help people having difficulties with the system. “These are intelligent people . . . attorneys, consultants. They work for nonprofits. My initial response when they come to me is, ‘It’s going to be a long process, and I, as your broker, may not be able to complete it.’ ”

Kofman readily acknowledged that the site remains a work in progress. She said many of the District’s international residents end up having to complete a “frustrating” identity check in person, while wait times with the exchange’s call center can sometimes last an “unacceptable” two hours or more.

But she said most residents can log on, check for federal subsidies, select plans and obtain a confirmation of their choice, making the city’s exchange a “model” compared with many others.

“Like Apple’s launch of the iPhone,” Kofman suggested, the District’s exchange would get better with every upgrade. The next one is planned for February, when residents who forget their user names or passwords will be able to retrieve that information online rather than be required to call customer service.

Yvette M. Alexander (D-Ward 7), chairwoman of the D.C. Council’s Health Committee, applauded the exchange’s launch overall. Council member David Grosso (I-At Large) said he was pleased that the District could “handle its problems in-house” compared with Maryland, which has had to spend millions on outside help and may need to turn over part or all of its exchange to the federal government or a better-functioning state while it makes necessary fixes.

Alexander said she has received warnings that problems remain. She read a recent e-mail from a resident who said she had been left without insurance for the first time in her life because the District’s exchange apparently had not communicated her insurance selection to her chosen provider:

“I played by all of the rules and signed up for a much, much more expensive plan. Printed the confirmation . . . and now have spent countless hours on hold,” wrote Erica Mueller. “I have no insurance. . . . This is insane. I am beyond furious.”

Nearly 60 percent, or 11,967 of the city’s enrollees, came into the system through its small-business marketplace, the same part of the system many congressional staffers must use to buy health care.

Grosso asked Kofman how many of the total were Hill staffers, but Kofman replied that such information is confidential. She said only that it was “more than 50 percent” of the total.

Grosso, a former congressional aide, suggested that the number could be a good barometer of how the city’s exchange is functioning.

Hill staffers, he said, will compare notes. “If the word is, ‘The exchange was fine, I got coverage there,’ you will see an uptick,” he said.