Sen. Joe Manchin, D-W.V., is a conservative Democrat who has voiced his share of complaints about the troubled.
He's criticized the website problems that have stymied consumers shopping for health insurance on HealthCare.gov, the federally administered website that allows people in 36 states to comparison-shop health insurance plans. He's evenof the IRS penalty for people who neglect to purchase insurance.
Yet despite his criticism, he doesn't think Health and Human Services Secretary Kathleen Sebelius, whose agency bears ultimate responsibility for overseeing the law's implementation, should be forced out of her job as a result of the rocky start.
"I think she should stay," he told ABC's "This Week" on Sunday. "And I think she will get the job done."
When Sebelius was asked on Thursday about those who have called for her dismissal, her response verged on pugilistic: "The majority of people calling for me to resign I would say are people who I don't work for and who do not want this program to work in the first place."
Manchin said that comment was "unfortunate," but he added, "I think Kathleen was successful as an insurance commissioner in Kansas, she was a successful governor working with both sides of the aisle. She's very capable of bringing people together."
Manchin's response has been typical of Democrats who have sought a middle ground by criticizing the law's rough debut and demanding accountability while trying to avoid piling on an administration that's already under fire from all sides.
"Anyone who got paid by the taxpayers, whether it's those private contractors who got taxpayer money, whether it's the health agency personnel who got money, or whether it's members of Congress who are responsible for the oversight of this plan, everyone should be accountable," said Rep. Xavier Becerra, D-Calif., on "Fox News Sunday."
"But the most important thing right now is making sure we fix the website not fixate on the website," he added.
Sen. Jeanne Shaheen, D-N.H., who has offered a proposal to extend Obamacare's open enrollment period,but when she was asked on CBS' "Face the Nation" whether she still has confidence in Sebelius, she dodged the question.
"I think it's too early to start placing blame," she said. "I think we need to get the marketplaces working, we need to get the website working, and we all ought to be focused on how we make sure that the people who want healthcare in this country can get enrolled and be covered."
"There's going to be plenty of time to place blame on who was responsible for whether it should have worked on day one or didn't work or whatever," she added. "But right now everybody's goal should be, let's get this working."
Republicans, however, have not been shy in directly blaming Sebelius for the technological problems that marred the launch of the online marketplace, with some demanding her immediate ouster.
While he stopped short of outright calling for Sebelius to step down, Rep. Darrell Issa, R-Calif., said on CBS' "Face the Nation" that she should leave if she can't rectify the mistakes that occurred under her watch.
"The President has been poorly served in the implementation of his own signature legislation. So if somebody doesn't leave and if there isn't a real restructuring...then he's missing the point of management 101, which is these people are to serve him well and they haven't," he said. "If [Sebelius] cannot reorganize to get the kind of a team in consistently to meet his agenda, then she shouldn't be there."
Rep. John Fleming, R-La., who sent a letter to the president on Thursday, signed by 33 GOP congressmen, calling for Sebelius to step down, continued his criticism of the secretary on Sunday, telling CNN that she's been the law's "biggest cheerleader."
"Americans both Democrat and Republican demand accountability, and Secretary Sebelius is obviously not taking accountability for this," he said. "She says the people who want her to resign she doesn't work for. I hate to tell you, but I'm a taxpayer. She works for me. She's a public servant."
"We tried to tell her all along," Fleming said. "She was the biggest cheerleader for this. Please, let - work with us. Let's work together in cooperation. And instead, she said, no, we don't want to hear from Republicans on this."
Rep. Marsha Blackburn, R-Tenn., said the level of "incompetence" displayed by the website launch is "staggering" on "Fox News Sunday."
"When I am talking to health care officials and constituents," she said, "they're saying, 'How can you expect the government to handle one sixth of the economy when there is this type of staggering in incompetence on a website rollout?'"
As for Sebelius' role in the rollout and whether she should face punishment as a result, Blackburn would only say, "Well, we want her to talk with us before she is out the door."
On Wednesday, Sebelius will get the chance to do just that when sheduring testimony before the House Energy and Commerce Committee.