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Pressure is rising on the president to make heads roll for ObamaCare’s botched rollout.

The White House on Monday said departures are always possible but rejected the idea that these would be connected to the fiasco engulfing President Obama’s signature legislation.

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That official line, offered by press secretary Jay Carney, followed comments from two former advisers to Obama that people responsible should be thrown overboard.

“I think the only way to restore ultimate confidence going forward is to make sure that whoever was in charge of this isn’t in charge of the long-term healthcare plan,” Robert Gibbs, Carney’s predecessor as White House spokesman, told NBC News.

Former senior adviser David Plouffe also suggested change could be coming.

“I think once the website gets fixed, and it will, then you have to step back and say, ‘OK, what do I need to have confidence going forward that I can to implement this law?’ ” he said during an appearance on ABC News.

The remarks were notable coming from two former members of Obama’s inner circle, who have continued to advise the president from outside the White House.

Asked about the remarks, Carney said people could leave the president’s team but that this should not be seen as an act of retribution for failure.

“Personnel changes happen all the time,” he said at his daily briefing. “I wouldn’t necessarily associate any particular one with, you know, any incident.”

Carney repeatedly said he had no personnel decisions to announce or even preview, saying the White House was not focused on Monday morning quarterbacking on the healthcare rollout.

Asked if there was a time when Obama would shift his focus to accountability for the problems, he said, “Well, you know, hypothetically, you could say that.”

It is not clear whether Carney was being coy or simply doesn’t know whether departures from Obama’s health team could be coming.

While Plouffe and Gibbs are seen as Obama insiders, Carney is not an Obama original and is not considered a member of the president’s inner circle.

Congressional Democrats are frustrated with the administration’s performance, not only because of the Affordable Care Act website but because of the millions of people who have been told their health insurance policies are being canceled despite Obama’s promise that people who like their plans could keep them.

On Friday, 39 Democrats broke with the White House to back a Republican bill allowing insurers to offer limited policies that were canceled because of the new law’s more stringent requirements.

Comments from Gibbs and other ex-advisers from Obama’s first-term team suggest they realize ObamaCare’s problems are threatening not only the president’s second term but also his legacy.

The White House has started an internal assessment of what went wrong, according to The Wall Street Journal, and Obama has said there will be “a lot of evaluation” about the misfires that led up to Oct. 1, the date the exchanges launched.

Obama so far has stood by Health and Human Services (HHS) Secretary Kathleen Sebelius, the public face of the healthcare exchanges, noting several times that her expertise is not in the technical side of HealthCare.gov.

Yet there could be a political danger to sticking with Sebelius for too long — particularly if Democrats in Congress grow antsy for a scalp.

Former President George W. Bush fired then-Defense Secretary Donald Rumsfeld shortly after the 2006 elections, which saw Democrats recapture majorities of the House and Senate.

Some Republican lawmakers were flabbergasted at the timing of Rumsfeld’s dismissal, as they argued Bush might have saved some seats by taking action sooner and showing he realized his administration’s leadership of the Iraq War had been faulty.

Obama and Democrats now fear they could lose their Senate majority because of HealthCare.gov.

A big problem for Obama, however, is that it could prove difficult to confirm any replacement for Sebelius. If she were to leave, the department could lack anything more than an acting head for some time.

Obama has been reluctant to remove top officials in the past, but has done it in response to serious problems at various agencies.

In 2012, the head of the General Services Administration resigned and two other officials were fired after an investigation into excessive spending at agency conferences. Another four officials were placed on administrative leave.

Earlier this year, Steven Miller, the acting director of the Internal Revenue Service, resigned after the agency admitted it had targeted conservative political groups seeking tax-exempt status.

At the time, Obama described the move as necessary to “help restore confidence going forward.”

Cal Jillson, a professor of political science at Southern Methodist University, said Obama would benefit from dismissing Sebelius or one of her key deputies as soon as possible.

“Firing someone can be very beneficial to an administration because it shows a forceful, affirmative response to a problem, identifies a culprit and displaces blame from the president to one of his appointees,” he said.

If Obama does decide to shake up his team, it’s likely a decision won’t happen until after Nov. 30, the administration's self-imposed deadline for fixing HealthCare.gov.

If Obama does decide to shake up his team, it’s possible a decision won’t happen until after Nov. 30, the administration’s self-imposed deadline for fixing HealthCare.gov.

The website has visibly improved since its debut, but can still only handle up to 25,000 concurrent users — half the intended capacity.

There may be little reason for Obama to make personnel changes until after the administration can assess how the website is working at the end of the month, because a working website could alleviate some of the political pressure on the White House.

This story was posted at 4:54 p.m. and updated at 7:54 p.m.