Several state-run exchanges, such as those in California, New York and Kentucky, have been reporting robust enrollment, while states that rely on the federal site have lagged far behind.
But enrollment counselors in California said the state website was slow or unresponsive Monday, often making an application take up to two hours to finish. Wait times to state call centers stretched beyond an hour in some cases, according to Covered California.
Gil Alcala, a state-certified insurance agent in Covina, said he worried about 25 applicants possibly falling through the cracks because the Covered California website wouldn't let him input data from their paper applications Monday.
"The website is freezing and then I get an error notification," Alcala said. "They need to push this deadline back again. This is terrible."
California officials said they were sticking with the Dec. 23 deadline, but they vowed to help anyone who starts an application Monday to get coverage starting Jan. 1.
"We will help people get across the finish line who have started an application [Monday]," Lee said. "If you have made a good-faith effort to get started, you can finish it [Tuesday]."
Los Angeles resident Jeff Norman, 54, tried to beat the deadline and applied last week for Medicaid coverage. But he said he still hadn't received confirmation of insurance starting Jan. 1. His current coverage through Anthem Blue Cross is being canceled Dec. 31 because it didn't meet all the requirements of the healthcare law.
Norman needs regular physical therapy on his aching hip and leg, he said. "If I want to get medical services at the beginning of January," he said, "I don't know what will happen."
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Times staff writer James Barragan contributed to this story from Los Angeles