(Reuters) — President Barack Obama has "full confidence" in Health and Human Services Secretary Kathleen Sebelius despite the troubled launch of the U.S. government website for signing up for his signature health care insurance program, the White House said on Tuesday.

Americans trying to shop for health insurance at healthcare.gov under Obama's health care law have been frustrated by error messages, long waits and system failures, with many failing to make it through the system despite repeated tries.

Online insurance exchanges were launched on Oct. 1 under the 2010 Patient Protection and Affordable Care Act, often called "Obamacare," to offer health care insurance plans to millions of uninsured Americans.

Former White House spokesman Robert Gibbs, who remains close to the White House, said the administration should "fire some people" for the problems, and Sen Pat Roberts, R-Kan., has called on Ms. Sebelius to resign.

"The secretary does have the full confidence of the president," White House spokesman Jay Carney told reporters, referring to Ms. Sebelius.

Her department is in charge of rolling out the online insurance exchanges, a key part of a law vigorously opposed by Republican lawmakers and other U.S. conservatives.

Ms. Sebelius, the former governor of Kansas who has served as HHS secretary since April 2009, has played a prominent role in publicizing the launch of the exchanges.

"She, like everyone else in this effort, is focused on our No. 1 priority, which is making the implementation of the Affordable Care Act work well," Mr. Carney said.

"People are working 24/7 to address the problems and isolate them and fix them when it comes to the website and enrollment issues," Mr. Carney said.

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When the website healthcare.gov went live on Oct. 1, President Obama told Americans it would be as easy to compare the cost of insurance plans as it is to "shop for a plane ticket on Kayak or a TV on Amazon."

The administration initially characterized the problems as "glitches" that it said were not surprising given that 14.6 million people checked out the site in its first 10 days.

But the problems have turned out to be more complicated than mere traffic issues, with outside technology experts saying the system's architecture was poorly designed.

The government has not yet revealed how many people have successfully signed up for insurance.

Experts say the administration has until mid-November to iron out the problems or risk jeopardizing its goal of signing up 7 million people in the first year of the health care law's marketplaces.