By David Morgan and Curtis Skinner

WASHINGTON/NEW YORK (Reuters) - Americans trying to find out how much health coverage will cost under Obamacare endured a third day of limited access to new online health insurance exchanges on Thursday, leading to a growing backlog of people waiting to enter the system.

Health clinics and other nonprofit groups that offer in-person assistance reported unexpectedly high numbers of walk-in visits and phone calls from potential enrollees, who were unable to enter federal and state marketplace websites that were overwhelmed by millions of online hits.

The high number of log-ins have heartened administration officials and Obamacare supporters, as a possible early sign that President Barack Obama's signature healthcare reform will prove successful in signing up millions of the uninsured over a six-month enrollment period that ends on March 31.

But continued delays and glitches have caused increasing frustration for those eager to begin enrollment.

The Borinquen Health Center in Florida said only about 5 percent of the nearly 400 people who sought guidance in a 48-hour period were able to access Healthcare.gov, the website portal for consumers in 36 states where the federal government is operating exchanges, also known as marketplaces.

Some uninsured people have filled out paper applications that will prolong the enrollment process by weeks. Organizers say most are content, however, to learn about benefits including federal subsidies and provide their contact information so they can act later when the online system improves.

"There have been so many issues with online enrollment because of glitches. But we've been able to take down a ton of information from people so that they can come back and complete the process as soon as the computer glitches get resolved," said Andy Behrman of the Florida Association of Community Health Centers, which has 50 facilities in Florida.

The U.S. Department of Health and Human Services said on Thursday that 7 million visitors had logged on to Healthcare.gov. A federal call center has also fielded 295,000 telephone calls. The administration does not expect to release enrollment data until mid-November.

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To share your experience with the online exchanges, see: https://www.surveymonkey.com/s/ReutersExchanges

Officials are quick to emphasize that the number of website hits is unlikely to bear any correlation to a much smaller number of actual enrollments in the exchanges' first week. But they expect the number of Americans completing applications to spike in November and December for people intent on having benefits available on January 1.

Technical experts worked around the clock to expand the capacity of the federal system. Officials said improvements reduced the number of people stuck on hold by about one-third. But by Thursday afternoon, visitors seeking to set up an account on Healthcare.gov were still running into web pages asking them to wait.

KEEPING TRACK OF THE INTEREST

State-run exchanges said they were seeing tangible improvements in allowing residents to access their websites after a rocky start for many during Tuesday's launch.

At least eight of the 14 states operating their own exchanges reported no significant problems on Thursday. They are California, Colorado, Maryland, Kentucky, Massachusetts, Washington, Rhode Island and Vermont.

"I'd say the experience for users right now is good," said Rebecca Pearce, executive director of Maryland's exchange. "I'd say we're doing well."

The exchanges in California and Washington have undergone overnight maintenance in recent days to improve functionality.

In Maryland, early glitches have led at least some enrollment assistors, or navigators, to help consumers fill out paper applications to get the enrollment process started.

"I know they're working very diligently, and it's getting better every day. But it's not quite where it needs to be," said Kathleen Westcoat, chief executive of HealthCare Access Maryland, the navigator connector for the Baltimore region.

Other organizations at the grass-roots level have begun finding ways to keep track of the uninsured who have not been able to get through.

"For folks who've had trouble enrolling, the most important thing is that someone's there to answer questions and make an appointment for next week to go through the process," said Anne Filipic, president of Enroll America, a nonprofit group at the forefront of Obamacare's outreach to the uninsured.

Gateway to Care, a small nonprofit healthcare organization headquartered in impoverished southeast Houston, has received scores of telephone calls from people wanting to learn about their options under the law. Many of the callers live outside the group's county-wide service area.

"It's really unexpected. We thought we were going to have to really beat the bushes to get people interested," said Gateway to Care's executive director, Ron Cookston, who has had 15 of his 19 staff members trained as Obamacare application counselors.

One health center in Miami managed to enroll 68 people for subsidized coverage through Healthcare.gov. The center's staff also had to turn away 24 people who cannot obtain health coverage in Florida because its Republican-controlled Legislature has not agreed to join Obamacare's Medicaid expansion for the poor.

"That really, really bothers me," Behrman said.

But many are content with the thought that they can enroll sometime down the road. "People understand that we'll be enrolling them later in the month. People are happy to just get that information," said Dr. Ibraham Ahmed of Community Bridges Management, which is helping guide would-be enrollees in southeastern Michigan.

(Additional reporting by Lewis Krauskopf in New York; Editing by Michele Gershberg and Peter Cooney)