“The back end is so backed up, and no one can give me an answer,” said Gallo, a strong supporter of President Obama’s healthcare law. “What happens if we don’t get coverage by Jan. 1? There are real problems here.”

Consumers’ anxiety has grown as they endure long waits on the phone, computer errors and conflicting answers from the state and insurers about their coverage. The average wait time at the state’s call centers climbed to 36 minutes last week, and California is still trying to clear a backlog of paper applications filed in October and November.

State officials say the huge demand for insurance is a positive sign for the rollout of the Affordable Care Act. They acknowledge there have been delays, but they say the vast majority of people are enrolling smoothly and getting their first insurance bills. The state said it didn’t have exact figures on how many customers are still waiting for proof of insurance.

“With the large numbers we are dealing with, there will be some individuals who don’t get ideal service,” said Peter Lee, executive director of Covered California. “We are committed to make sure everyone who wants insurance gets it Jan. 1.”