The healthcare.gov website has been plagued by problems since it launched on Oct. 1.
At a news conference in Raleigh Thursday, Senator Hagan said she doesn't understand why there have been so many issues with the site.
"I'm unbelievably frustrated. Here in the U.S. we ought to be able to produce a website that can be accessible by people in the country, and we need to get it fixed ASAP."
Hagan said she's asking the Obama administration to extend the open enrollment period by two months, and waive the penalty for the individual mandate for the same period of time, to make up for time that is being lost while the website for the federal exchange is not functioning.
Hagan is among 60 Democrats who voted for the healthcare reform law in 2009.
The leading contractors who built the troubled health insurance website told Congress Thursday that the government failed to thoroughly test the complicated system before it went live.
Executives of CGI Federal, which built the federal HealthCare.gov website serving 36 states, and QSSI, which designed the part that helps verify applicants' income and other personal details, testified under oath before the powerful House Energy and Commerce Committee.
The contractors said they each tested their own components independently but that the Health and Human Services department was responsible for testing the whole system from end to end. That kind of testing didn't happen until the last couple of weeks before the system's Oct. 1 launch.
It quickly crashed once consumers tried to use it.
The administration's determination to go live on Oct. 1 despite qualms about testing quickly became a focus of the hearing, which turned sharply partisan at times.
Republicans, still committed to repealing Obama's health care law, approached the questioning with a prosecutorial tone, leading New Jersey Democrat Frank Pallone to call the whole exercise a "monkey court."
North Carolina Representative Renee Ellmers was sharply critical.
"The president on Monday in the Rose Garden gave a speech and because of the glitches, I call them gaffes, they're much bigger than glitches I believe, glitches are little hiccups and these are much more than little hiccups," she said.
The contractors did say the problems can and are being fixed on a daily basis, and they expressed confidence that uninsured Americans would have coverage by Jan. 1, when the law's benefits take effect, though they would not be held to a timetable.