House Speaker John Boehner criticized the Obama administration's plan to disable a key part of its health overhaul website this weekend to resolve glitches that overwhelmed the launch of new health insurance markets.

“The news that its enrollment system is already going offline confirms that the launch of the president’s health care law has been an unmitigated disaster," Boehner said in a statement Friday.

The Health and Human Service Department is using overnight hours this weekend to debug the system. The department did not release a schedule for hours of operation, but a spokeswoman said the site would be taken down at 1 a.m. EDT each night for a few hours. 

Boehner blasted the White House for dismissing the technical problems as glitches and not disclosing how many Americans were able to sign up for plans using the "fatally-flawed system."

"This announcement is more proof that we need to delay the law and provide basic fairness, just as Republicans have called for. How can this administration tax individuals for not purchasing a product from a website that doesn’t even work?," Boehner said in the statement.

An effort by congressional Republicans to defund or delay the health care law led to an impasse with Democrats over passing a budget bill, and that sparked a partial government shutdown Tuesday. Other Republicans joined Boehner in his criticism of the website problems.

"Americans have seen once again that ObamaCare is not ready for prime time," Rep. Eric Cantor of Virginia, the No. 2 House Republican, said in a statement Friday. "A dysfunctional website is the least of that law's problems."

The administration put the best face on the situation, noting the unexpectedly strong interest from millions of consumers.

"Americans are excited to look at their options for health coverage, with record demand in the first days of the marketplaces," said the release announcing the planned fixes.

The statement was headlined: "Health Insurance Marketplace Open for Business - Week One Success."

The state-level markets were designed to be the gateway to health insurance for people who don't have access to coverage on the job. Middle-class consumers will be able to buy government-subsidized private plans, while the poor and near-poor will be steered to Medicaid in states agreeing to expand the program.

Federal and state websites experienced problems this week.  Some states, including Maryland, have also announced they are scheduling repairs.

The federal site, which serves 36 states, drew millions of users, an indication of strong consumer interest. Yet many people were unable to get on the site. They encountered a screen that told them to wait, and they did, sometimes for hours. Refreshing the screen only sent them to the back of the line.

Quite a few got hung up trying to create security questions to protect their accounts. The drop-down menus providing the questions would not populate. As a result, consumers could not advance through the application process and learn if they were eligible for a tax credit to help pay premiums, much less pick a plan.

Some who did make it through were timed out because they took too long comparing plans.

At the end of the first day at most a handful of people had managed to successfully enroll through the federal site.

However, by Friday, enrollments seemed to be picking up -- though not yet at desired levels. The administration is not releasing numbers.

"We are pleased that enrollment for health care coverage through the new marketplaces is picking up," the Blue Cross and Blue Shield Association said in a statement. "We expect enrollment to continue to increase."

The so-called Blues are major players in the individual insurance market, but some smaller insurers have yet to see any new customers.

By Monday, "there will be significant improvements in the online consumer experience," HHS said.

The upgrades include extra capacity for more users to get into the system, more technicians working round-the-clock to fix problems, and new pathways to get to the application faster. No details were given. Call centers are also getting more staff and HHS said wait times are now down to less than a minute.

The administration previously announced it is adding equipment to handle the high volume of users. Now it looks like software fixes are also needed.

Consumers have until Dec. 15 to enroll for coverage that starts Jan. 1.

The Associated Press contributed to this report.