Some people are successful.
Others find they need more documentation or further help to solve problems.
"I've had two of my kids to the doctor twice this month. And I had to pay out of pocket, because they are saying they are inactive, and they are active, so I just, don't know what to do," said Melissa Manning of Louisville.
The glitch already has cost Manning money. A counselor at Americana helped, but could not resolve the problem, Manning said.
Kentucky Gov. Steve Beshear said Monday that 182,000 Kentuckians have signed up through Kynect since October 1.
That's roughly 1,500 people a day, and more than one quarter of the number of Kentuckians who did not have health insurance in 2011 and 2012, according to federal figures.
Three-quarters of those who've enrolled take Medicaid; the rest, private health insurance.
"That just shows you the pent-up demand that Kentuckians have for affordable health care here in Kentucky," Beshear said Monday.
Counselors expect to be busy through March 31, when people must prove they have health insurance or pay a fine through their taxes.
Most Kentuckians have health insurance through their employers.
The enrollment numbers for the rest -- and very few online glitches -- brought Kentucky national attention -- and the governor a seat at the State of the Union address Tuesday.
It's just three years after he told lawmakers it was time to get President Obama "off our backs" on issues like coal.
"So, next November 80 percent of Kentuckians will know that it doesn't affect them, and it won't be an issue for them. And a good part of the other 20 percent are going to be covered either by expanded Medicaid or by a qualified health plan, and they are going to like very much what they are getting for the dollars that they pay," Beshear said.
"Our work in providing access to health care will strengthen our families as well as our workforce," Beshear said in a statement released after the State of the Union speech Tuesday night.
Critics say the plans on Kynect are too expensive and cost more than private plans people may have had last year.