Weeks of frantic technical work appear to have made the government’s health care website easier for consumers to use. But that does not mean everyone who signs up for insurance can enroll in a health plan.

The problem is that the systems that are supposed to deliver consumer information to insurers still have not been fixed. 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 will not be feasible if data is missing for tens of thousands of consumers.