For every individual who did sign up, there were others who resembled Mr. Huber: people who have decided to stay uninsured for now, despite the law’s requirement that most Americans get coverage this year or pay an income tax penalty of $95 or more.

A common thread running through stories of the unenrolled is cost. Many people either do not qualify for federal subsidies or believe that the assistance is not enough to make insurance affordable, interviews with consumers and experts suggested. According to enrollment counselors in several states, people who have gone without health insurance or major illness for years can be especially resistant to investing in coverage.

To be sure, some of those who chose not to sign up were motivated by ideological opposition to Mr. Obama, to the law’s mandate that they buy insurance, or to both. And for many others, confusion and lack of understanding, including about whether they could get financial help buying coverage, were the overriding reasons…

Declaring himself impatient and not good with computers, Mr. Huber said he had become flummoxed when trying to explore Kynect, Kentucky’s insurance marketplace, including late last month, when the online application form would not accept his phone number. He did not know that he could have sought enrollment help, he said.

“I tried four times and said, ‘Forget this,’ and logged off,” he said.