WASHINGTON — As the criticism over the White House’s handling of domestic violence allegations against a former top aide continues to grow, so does rampant speculation that John Kelly’s days as chief of staff are numbered, according to multiple people familiar with the discussions.

Kelly, a no-nonsense retired four-star Marine general, was brought on last summer to instill military-style discipline in a White House fraught with leaks and disorganization. Now, the contradictory public and private accounts offered up about how he handled the accusations against former staff secretary Rob Porter have chipped away at his credibility — and raised even more questions.

Among them are new concerns about how classified intelligence is handled within the White House. The distribution list for the President's Daily Briefing, which contains highly classified information, is wide and includes many staffers who do not have permanent security clearances, according to a source with first-hand knowledge who was “really concerned with how liberally classified intelligence was being shared.”

Three people close to President Donald Trump tell NBC News that he has not sanctioned a formal search for a successor to Kelly and may decide to keep Kelly in his position. Allies close to Kelly insist the president’s support for him is unwavering and that Kelly will report for duty for as long as the president wants him there.

But Trump has also reached out privately to friends to solicit opinions on a possible replacement, according to two people familiar with the president’s thinking.

Among the names the president is considering are his chief economic adviser, Gary Cohn; the House majority leader, Rep. Kevin McCarthy, R-Calif.; and Mick Mulvaney, director of the Office of Management and Budget, according to multiple sources.

Mulvaney dismissed reports that he is under consideration, telling CBS’s “Face the Nation” on Sunday: “You think that maybe someone would have mentioned it to me. No one's talked to me at all. Not a single time."

Likewise, McCarthy told reporters Wednesday that he has “never” spoken to the president about the position, adding that there was “no job opening” at the White House.

Vice President Mike Pence on Wednesday became the highest-ranking administration official to offer up a ringing endorsement of Kelly.

"There are very few Americans or American families that have served this nation more honorably or have sacrificed more for this country than the family of Gen. John Kelly,” Pence said in a forum when asked about the criticisms and questions about Kelly’s tenure. “His distinguished service as chief of staff gives me and the president great confidence in this good man.”

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"John Kelly has done a remarkable job as chief of staff," Pence added, "and I look forward to continuing to work with him for many, many months to come."

The president himself has not publicly said anything to prop up Kelly, instead tweeting about due process for those whose “lives are being shattered and destroyed by a mere allegation” — presumably a reference to Porter.

When reports of the abuse allegations first emerged in The Daily Mail last Tuesday, on Feb. 6, Kelly came out strongly in support of Porter and was effusive in his praise. A day later, Kelly issued a statement saying that "there is no place for domestic violence in our society," but that he stood by his original comments. The White House said last Thursday that Kelly had just learned the full extent of the accusations from the media reports.

Then, on Friday, Kelly instructed White House staff that when he was briefed on the abuse allegations against Porter by his two ex-wives, Porter was “gone 40 minutes later.”

It later emerged that a limited briefing had been arranged by the White House for select reporters in which Porter addressed the allegations against him and explained his version of the story. Sanders later clarified that Kelly and Porter had "a conversation" within 40 minutes, but that Porter was out of a job within 24 hours, not 40 minutes.

The White House’s latest account of the events leading to Porter’s exit now appears to be crumbling.

Sanders on Tuesday insisted that the White House personnel security office “had not made a final recommendation for adjudication” in regards to the allegations of abuse, which were flagged by an FBI background check of Porter. But a former senior White House official said that that office compiles information on staff members and, while the office may raise questions about an individual, the final decisions belong to senior White House staff.

Typically, once the FBI background checks are completed, it’s up to the White House political staff to then determine how to proceed with any individuals the bureau regards as a potential target of blackmail.

In congressional testimony Tuesday, FBI Director Chris Wray revealed that the bureau had finished its report and delivered its findings to the White House long before Porter’s exit.

Porter, a rising star in Washington, resigned Thursday after his two former wives publicly accused him of verbal and physical abuse. Porter has denied the claims against him.

The publication of the accusations led to revelations that Porter, whose job was to handle all classified materials sent to the president, had been working without a permanent security clearance, raising red flags about the kind of sensitive information he was privy to.

“Porter got everything. He got stuff [CIA Director Mike] Pompeo doesn’t get,” a person with direct knowledge of the process said, in reference to the fact that Porter received intelligence gathered by multiple agencies.

The White House has not revealed whether other senior staff members, including White House counsel Don McGahn or the deputy chief of staff for operations, Joe Hagin, were also made aware of concerns raised by Porter’s security clearance early on. Sanders said she was not aware that any issues were brought to McGahn or Hagin specifically.

Individuals in their positions would typically be notified of clearance-related issues, according to multiple former administration officials.

In a White House that has been rife with firings and resignations, any further shakeups could come at a great cost, both to the president’s ability to execute his agenda and for the Republican Party as it heads into a midterm election.

Adding to the GOP's woes, the president’s popularity remains low early in his second year, the stock market has been volatile, and investigations by the FBI and Congress press on into both the president and his 2016 campaign for possible collusion with Russia.

Kelly is the second person to hold the powerful chief of staff position, having replaced Reince Preibus, who was let go after just 190 days on the job, after months of speculation that the president had lost confidence in him.

Kelly was a surprise choice when he took the job in late July amid an extraordinarily turbulent period, but the retired Marine general quickly imposed welcomed discipline and became a leading voice within the president’s inner circle.

But on the job for almost eight months, Kelly has also created additional headaches for the administration.

In recent weeks, he characterized some immigrants as “lazy,” and last fall, he criticized a congresswoman who was present during the president’s phone call with a Gold Star widow. Kelly has also suggested that the Civil War could have been averted by a compromise on slavery.

Now, his management of, and shifting story around, a top White House aide accused of physically assaulting two ex-wives has raised questions about his management style and integrity.