He added: "Although the glitches are unacceptable, so is the idea of leaving millions of Americans on their own, including families across the country who now have access to health care that they did not have."
The chairman of the Republican National Committee, Reince Priebus, has called for the resignation of Kathleen Sebelius, the administration's secretary of health and human services.
And the Republican-led House Energy and Commerce Committee will hold a hearing next week to examine what it calls Obamacare's troubled rollout. Sebelius has so far declined to testify, the committee said.
(Read more: Poll sizes up Obamacare tech hurdles)
"Secretary Sebelius had time for Jon Stewart, and we expect her to have time for Congress," said Rep. Fred Upton, R-Mich., and the committee chairman. Stewart grilled Sebelius earlier this month on "The Daily Show" for the glitches.
USA Today, citing technology experts, reported that the site was built using 10-year-old technology and may require constant fixes for the next six months and eventually an overhaul of the whole system.
Luke Chung, who owns a software and database programming company, told NBC News that the problems are serious.
"It doesn't work," he said. "It's supposed to get you a quote. It doesn't do that."
If it were his own product, he said, "I'd be embarrassed and I'd use language with my development team that couldn't be on the air. This is ridiculous."
But Gail Wilensky, a former director of Medicare and Medicaid who is now a health-care analyst, said that CGI was forced to deal with last-minute design changes ordered by the government, hampering CGI's ability to test the site.
Last June, a GAO report foreshadowed those problems, warning that the website might not be ready to go live, in part because of all the last-minute design changes.
(Read more: Low-Bamacare: Few enroll for Obamacare)
CGI has also helped establish some state websites that have received good reviews.
Based on Montreal, CGI has 69,000 employees in 40 countries, and is no stranger to large government contracts. Besides healthcare.gov and the province of Ontario, CGI lists on its website customers as varied as New York City, California, the Defense Department and the State Department.
In the quarter that ended June 30, the company reported revenue of $2.5 billion, more than double the same quarter in the previous year.
—By Tom Costello and Erin McClam, NBC News.