Stephen K. Bannon, one of President Trump’s top allies, threw a party in January at his Capitol Hill townhouse for the Washington bureau chief of Breitbart News, Matt Boyle. The usual guests from the right-wing media ecosystem were there in full force, but one attendee stood out: Mr. Trump’s national security adviser, Michael Waltz.

Mr. Waltz, who posed for pictures with Mr. Bannon, Mr. Boyle and others, had been invited as part of an effort to rehabilitate him in an administration that was only eight days old. He was in a quandary faced by many Trump aides from the president’s previous administration. He had become too Trumpy to former Republican allies in the Washington political class, but not Trumpy enough to the president’s hard-core loyalists.

Even as Mr. Waltz has been in the middle of negotiations on a cease-fire between Ukraine and Russia, several people close to Mr. Trump now wonder if Mr. Waltz might be an early administration casualty. Others suggest that Mr. Waltz’s determination to align himself with Mr. Trump will save him from the fate that befell three of the four national security advisers in the president’s first term.

“Mike understands the chain of command, which gives him a leg up over H.R. McMaster and John Bolton, who were there to implement their own agendas,” said Ezra Cohen, who served on the National Security Council and in the Pentagon during the first Trump administration. “He knows his job is to execute the policies of the president.”

A case in point was Mr. Waltz’s response to Mr. Trump’s televised blowup at President Volodymyr Zelensky of Ukraine in the Oval Office last month.

Two days later on CNN, Mr. Waltz said Mr. Zelensky was “incredibly disrespectful” and questioned whether he was “ready to go to peace.” The day before on Breitbart Radio, Mr. Waltz compared Mr. Zelensky to an “ex-girlfriend that wants to argue everything that you said nine years ago, rather than moving the relationship forward.”