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 on Monday as counselors navigated the website’s pages with relative ease.

Click. Next page. Click. Next page. The website, HealthCare.gov, was working so well that Ms. 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,” Ms. Egozi said. “I think it will be great when it’s 100 percent.”

A little over a week after the deadline that President 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 actually choose one. In other cases, people were asked to try again later.