An estimated 8.6 million people have visited the sites since they opened Tuesday, officials say, but many people have been frustrated in their attempts to reach the sites, The New York Times reported Friday.
A New Hampshire insurance broker who wanted to help clients was among the exasperated would-be users.
"I have tried more than a dozen times, in the middle of the day and the middle of the night," said Thomas M. Harte, president of the National Association of Health Underwriters.
Federal officials have declined to say how many people have signed up for health insurance through the sites, known as exchanges. However, a section of the Web where people can apply for coverage will be upgraded over the weekend, the administration said. As a result, the sites will be unavailable for several hours both Saturday and Sunday.
Sen. John Cornyn, R-Texas, one of the opponents of the law, said while President Barack Obama called the problems "glitches," they were "systemic failures of the Obamacare exchanges -- obviously not ready for prime time."
House Speaker John Boehner, R-Ohio, said in a statement Friday the website problem "confirms that the launch of the president's healthcare law has been an unmitigated disaster."
The Department of Health and Human Services said the sites would go offline during "off-peak hours," adding that the upgrades would provide "significant improvements in the online consumer experience."
"We know some of you are having trouble getting to the application at the website HealthCare.gov and we are sorry for any delays. Thanks for your patience, and please keep trying!" officials at the Centers for Medicare & Medicaid Services, part of the U.S Department of Health and Human Services, said in a statement.
Those needing help with a marketplace application can contact the 24/7 call center, use the live chat function, or go to LocalHelp.HealthCare.gov to find an in-person assister in your community, CMS said.
Those who don't have health insurance provided by an employer have six months to enroll.
Notable deaths of 2014 [PHOTOS]