At Community Action of Nebraska, a nonprofit group with a statewide network of navigators, Roger Furrer has witnessed the problems up close. Most applicants he worked this week could not get to the screen that shows their coverage options. “That’s really problematic,” he said, “because if people are wavering already, they won’t always come back and follow through.”

Some navigators said it was hard not to feel discouraged, especially when their clients, locked out by the website, went home upset. “We have people who understandably say, ‘Well what the heck am I doing here if you can’t enroll me?’ ” said Ted Trevorrow, a navigator in Philadelphia who has not been able to enroll a single person yet. “I always want to say, ‘That’s a really good question.’ ”

Their experience remains markedly different from that in most of the 14 states that built their own exchange websites, where people are managing to sign up in much larger numbers. The remaining 36 states depend on the federal exchange.

Clients wary of the health care law can be especially intolerant of the website’s problems, Mr. Trevorrow said. “They’re incensed over the fact that the law would, as they see it, intrude on them to this degree and then not even perform,” he said.