Washington (CNN) President Donald Trump woke up Friday with a key campaign promise defeated and his staff in open warfare, the elements combining into a storm of chaos for a man who, six months into the job, is swiftly realizing the limits of his power.

Trump, who watched from his White House residence as the vote to repeal Obamacare failed in the dark morning hours, has this week alone run up against his own party on major legislation, a decision to bar transgender people from the military, and an attempt to push Attorney General Jeff Sessions from his job.

As the week closed, some of Trump's top aides were losing patience, both with their colleagues and with the President himself.

There is a growing sense around Trump that conditions are ripening for chief of staff Reince Priebus to leave his post -- though sources close to the embattled aide insisted on Friday that he's staying put until asked to leave.

"He isn't going anywhere," one person close to Priebus said, even as some of Priebus' allies have privately urged him to step aside rather than continue to bear the public indignity of being shamed by his colleagues. But there were no signs on Friday that he planned to step aside of his own volition.

Speculation about Priebus' future has long been a staple of the Trump White House, but his defiance comes in the face of waning support from key members of Trump's inner circle. Two sources familiar with the situation say Trump's family -- including daughter Ivanka Trump and son-in-law Jared Kushner, among the President's most trusted advisers -- have lost faith in Priebus. One of those sources says Trump's kin are urging the President to finally execute a long-pondered shakeup. The failure of the health care bill only adds fuel to that fire, the sources said.

Another Republican close to the White House echoed that sentiment, saying the collapse of health care has likely heightened the urgency of Priebus' departure, giving Trump more cover to push Priebus out.

The chief of staff's dramatic fight with new communications director Anthony Scaramucci -- in which Trump clearly took Scaramucci's side -- only escalated the sense that Priebus may soon be gone.

Despite the furor, however, a person close to Priebus denied he would soon leave. He traveled with the President on Friday to Long Island, where Trump was delivering remarks about the MS-13 gang. Scaramucci also flew aboard Air Force One with other top aides, including deputy national security adviser Dina Powell.

Yet Priebus, the source said, was not accepting blame for the health care failure, despite his role in the West Wing as the establishment Washington hand.

Support

Over the course of the week, Trump and his team avoided several opportunities to offer public support for the chief of staff. On Thursday, press secretary Sarah Huckabee Sanders could not say whether Trump had confidence in Priebus.

"We all serve at the pleasure of the President and if he gets to a place where that isn't the case, he will let you know," Sanders said.

And Trump himself did not rush to Priebus' defense when a vulgar screed from Scaramucci appeared on the New Yorker's website.

Priebus allies claim Scaramucci's profane outburst will make it difficult for him to gain the support of key Republican figures in Washington and statehouses.

Priebus has suffered from a lack of public defenders, at least at the White House. Among his closest White House allies, Sean Spicer, quit last week in protest of Scaramucci's hiring.

One of his closest friends, House Speaker Paul Ryan, sought to bolster Priebus on Thursday.

"All I would say is, as you know, Reince is a good friend of mine," Ryan said during his weekly news conference. "Reince is doing a fantastic job at the White House."

Speculation has also swirled around senior strategist Steve Bannon, the bombastic former chief executive of Breitbart, though his fate appeared less clear on Friday. In the New Yorker interview, Scaramucci proclaimed that unlike Bannon, he was not "trying to suck my own cock." Trump also did not defend Bannon. But the senior strategist remains a key conduit to Trump's conservative base and the right wing media, a valued asset in the West Wing.

Chaotic week

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A staff shakeup would cap a chaotic week for Trump, who passed the six-month point of his presidency without a major legislative win and with his approval rating at historic lows.

Even in a town controlled by his own party, Trump found himself constantly butting up to the limits of his own power, a sour reckoning for a billionaire businessman accustomed to wide unilateral power.

When Trump began publicly humiliating bit attorney general on Twitter, deeming him "beleaguered" and "very weak," the speculation among many in the White House and the halls of Congress was that Sessions' days were numbered.

But Republicans in the Senate -- where Sessions served until January -- pushed back, reprimanding Trump for the open display of animosity. The Republican chairman of the Senate Judiciary Committee, Sen. Chuck Grassley, warned on Twitter that his panel was too busy to take up consideration a new attorney general nominee.

Both Priebus and Bannon were among the White House officials who sought to sooth Trump's anger at Sessions, reminding him that the attorney general has been one of the most effective members of his Cabinet in advocating for and advancing his agenda.

After Trump abruptly declared over Twitter on Wednesday that the US military would ban transgender people from serving, the pushback came just as swiftly. Several Republican lawmakers insisted that any able-bodied American should be able to serve. The Pentagon said it wouldn't enforce any ban until further guidance came from the White House.

The harshest rebuke, however, came in the small hours of Friday morning, when Trump wasn't able to make good on his promise to repeal the signature legislative achievement of his predecessor. He was foiled not by Democrats but by three members of his own party.

Priebus was intimately involved in the pressure efforts on Capitol Hill to repeal the Affordable Care Act. But it was Trump himself who called Sen. John McCain of Arizona late Thursday evening hoping to sway his vote. He wasn't successful.

After fellow Republicans Sen. Lisa Murkowski of Alaska and Sen. Susan Collins of Maine also voted against passage of a slimmed down repeal measure, Trump dispatched his ire on Twitter.

"3 Republicans and 48 Democrats let the American people down," Trump steamed. "As I said from the beginning, let ObamaCare implode, then deal. Watch!"