"While it is disappointing that so many people have had difficulty accessing the online marketplace, the survey results show that awareness of the marketplaces has grown this fall, and those who initially struggled appear determined to try again," said Sara Collins, vice president for health-care coverage and access at Commonwealth Fund, and the survey's lead researcher.
Starting in 2014, nearly all Americans will be mandated to have health insurance coverage by President Barack Obama's Affordable Care Act by March 31, or face a tax penalty.
(Watch: Will Obamacare increase your premiums)
The majority of Americans already have insurance through their employer's group plans, their parents' insurance or through government-run Medicare insurance for the elderly, or Medicaid for lower-income people. But about 47 million people last year did not have insurance.
The federal site HealthCare.gov—which is selling insurance in 36 states—and the 15 online health exchanges being individually run by the remaining states and District of Columbia were set up to sell insurance to the uninsured, and to people who already were buying individual policies. All of the exchanges are offering a range of insurance plans from competing prices, but all will have new minimum covered benefits mandated by the ACA.
Officials have estimated that about half of the 7 million people they hope to sign up in the first year will be eligible for at least some subsidy to offset the costs of coverage because their adjusted gross income will be less than 400 percent of the federal poverty level.
—By CNBC's Dan Mangan. Follow him on Twitter