(CNN) -- The deal ending the shutdown may not have put a dent in Obamacare, but the battle over implementing the health coverage law is not over.
One venue that Republicans are turning to for leverage, starting next week: oversight hearings, beginning with some tough questions about why the rollout of the website for enrolling in health care exchanges is having so many problems.
"The American people deserve to know what caused this mess," said Rep. Fred Upton, R-Michigan, chairman of the House Energy and Commerce Committee. "Delays and technical failures have reached epidemic proportions."
Upton has already asked officials from the Department of Health and Human Services to brief his committee on the problems at a hearing scheduled for next Thursday. He also is asking them to turn over records of their communications with website contractors about the preparations for the site's launch, and the problems people have had trying to use it.
Additionally, the chair of the House Oversight and Government Reform Committee, Rep. Darrell Issa, last week wrote to Health and Human Services Secretary Kathleen Sebelius demanding information about the rollout problems. Joining him was Sen. Lamar Alexander, ranking Republican on the Senate committee on health, education, labor and pensions.
One issue has been the ability to log in to healthcare.gov. A senior administration official told CNN some users, especially those who signed up "early on," have been having trouble logging in, but the administration is working on a fix. There also was conflicting word on whether some passwords were deleted if they were created in the first week or so after the launch.
Sebelius concedes there have been implementation difficulties.
"I'll be the first to tell you that the website launch was rockier than we would have liked," she told an audience in Cincinnati on Wednesday, during her tour to promote Obamacare. But, she told CNN affiliate WLWT, "There are constant improvements under way, so that we are getting people in much more quickly."
Nevertheless, a couple of Republicans have called on Sebelius to resign.
"Enough is enough," said Sen. Pat Roberts, who has called for her to step down in spite of being a longtime friend of her family. "Secretary Sebelius has had three and a half years to launch Obamacare, and she has failed."
Rep. John Fleming of Louisiana tells CNN he is working to collect signatures calling for Sebelius to leave.