His letters asked the companies for all their communications with the agencies involved in the health care reform effort as well as with the Office of Management and Budget and Obama's executive office.
At least two committees in the GOP-led House have scheduled hearings this week and next to probe the rollout problems.
"Clearly there's problems with the website, but I would argue that the problems go much further than that," House Speaker John Boehner told reporters on Wednesday.
Officials from the contractors hired to create the website, including CGI, Serco, and Equifax, will appear on Thursday before the House Energy and Commerce Committee, with Sebelius scheduled to testify at another panel hearing next week.
Meanwhile, the House Ways and Means Committee has a hearing set for next week with the head of the Centers for Medicaid and Medicare Services, a division of the Health and Human Services department that oversees ACA reforms.
One question certain to come up is why the rollout wasn't postponed after warnings in pre-launch tests that the website would fail. Sebelius told CNN that further delaying health coverage for Americans who need it was not an option.
"There are people in this country who have waited for decades for affordable health coverage for themselves and their families," she said.
Meanwhile, administration officials will brief House Democrats about the health care law's implementation on Wednesday, which caused their Republican counterparts to demand their own briefing. There was no immediate word on a separate session for the GOP.
White House meeting
One White House official confirmed that health insurance industry leaders would meet with senior administration officials, including Sebelius, on Wednesday.
A possible topic would be extending or delaying the enrollment period due to the website problems to give people more time to sign up.
The White House and Sebelius insist that the process is improving and people are signing up, encouraging critics to let the six-month open enrollment period proceed.
In addition, Carney hinted to reporters earlier this week of possible relief for consumers if the problems persist, saying that people can't be fined for not having affordable health coverage next year if they were unable to obtain such coverage.
Conservative Republicans who forced the 16-day government shutdown that ended last week by linking a funding measure to demands to dismantle or defund the health care law now want to delay the creation of market exchanges -- a key component of the reforms.
At least one Democrat, Sen. Jeanne Shaheen of New Hampshire, also is calling for an easing of the enrollment deadline.
The ACA exchanges create large pools of buyers to make coverage more affordable for the almost 50 million Americans without insurance.
Robust enrollment is vital to the program's success. The exchange effort also depends heavily on attracting younger, healthier participants, who would tax the health care system less but still pay premiums. That would help insurers offer lower rates to older Americans with more health care needs.
If younger people don't sign up, rates won't increase immediately but It could cause insurers to raise them in the future or drop out of the exchanges because they cannot make the economics work.
The individual exchanges are expected to include about 15 percent of Americans, with the rest of the insured population covered by employer or other group plans.
Republicans, including House Budget Chairman Paul Ryan of Wisconsin, also call for Sebelius to lose her job over the rollout problems.
Sebelius said she works "at the pleasure of the president" and is committed to her job.
"I think my job is to get this fully implemented and to get the website working right," she told Gupta.