The troubles have led some members of Congress to call for the resignation of Health and Human Service Secretary Kathleen Sebelius, The Hill reported Friday.
"We need a Secretary who can admit when enough is enough," Sen. Pat Roberts, R-Kan., said last week in calling for her to resign after health insurance companies reported the online registration system had numerous glitches.
The full extent of the problem isn't known, but only a small number of consumers have completed the application process. HHS has declined to give actual numbers.
The House Energy and Commerce Committee has asked Sebelius to testify at a hearing next week. She has declined an invitation to attend, a response committee chair Fred Upton, R-Mich., called "wholly unacceptable."
Even comedian Jon Stewart has derided the start of the program. Interviewing Sebelius on The Daily Show, Stewart said, "I'm going to attempt to download every movie ever made, and you're going to try to sign up for Obamacare, and we'll see which happens first."
Republicans haven't been alone in their criticism of the program's fumbled start-up.
The current White House press secretary, Jay Carney, has admitted the president is "not happy" about the problems, but rejected calls for Sebelius to step down.
Even so, conservative activists are working to undercut the law on the state level, The New York Times reported. In Virginia, a group called Americans for Prosperity is campaigning against politicians who want to expand Medicaid under Obamacare.
Tim Phillips, president of the group backed by the billionaire Koch brothers, described AFP's work as "trench warfare." Targeting a Republican state legislator from a conservative district, AFP activists knocked on 2,000 doors, distributed leaflets and turned up by the hundreds at a commission hearing wearing the group's iconic green T-shirts.
So far, Americans for Prosperity has spent millions running similar campaigns in states across the country.
"I don't believe this fight is in Washington or ever was," says Jennifer Stefano, who runs AFP's Pennsylvania chapter. "I think this is a street fight. It's a man to man, so to speak, fight of going door to door."