And with coverage for many people scheduled to begin in just 30 days, insurers are worried the repairs may not be completed in time.

“Until the enrollment process is working from end to end, many consumers will not be able to enroll in coverage,” said Karen M. Ignagni, president of America’s Health Insurance Plans, a trade group.

The issues are vexing and complex. Some insurers say they have been deluged with phone calls from people who believe they have signed up for a particular health plan, only to find that the company has no record of the enrollment. Others say information they received about new enrollees was inaccurate or incomplete, so they had to track down additional data — a laborious task that would not be feasible if data is missing for tens of thousands of consumers.

In still other cases, insurers said, they have not been told how much of a customer’s premium will be subsidized by the government, so they do not know how much to charge the policyholder.