In conversations with allies inside and outside the White House, Mr. Trump, who rarely assumes blame for the crises he creates, has criticized his staff as serving him poorly. He has spared no one, including the White House counsel, according to two people who have had direct discussions with him.

According to associates of Mr. Trump, the president has become mistrustful of many around him amid a spate of leaks about West Wing dysfunction. He is relying heavily on his daughter Ivanka Trump and son-in-law, Jared Kushner, as well as his longtime spokeswoman, Hope Hicks, and his personal bodyguard turned White House assistant, Keith Schiller. He has also been reaching out to several old campaign aides; the campaign manager he fired in June, Corey Lewandowski, was spotted twice in the West Wing this week.

Ms. Trump and Mr. Kushner, along with Mr. Trump’s policy adviser, Stephen Miller, a former aide to Attorney General Jeff Sessions, were in the small cluster of aides with Mr. Trump at his golf club in Bedminster, N.J., during the May 5 weekend when he talked in earnest about firing Mr. Comey, according to two people briefed on the discussions. Mr. Kushner and Mr. Miller both supported the move. Mr. Kushner suggested to Mr. Trump shortly after a special counsel was named that he should consider striking back forcefully, people briefed on the deliberations said.

Some of Mr. Trump’s senior aides privately recognize that they may have to be restrained in making significant staff changes after his coming foreign trip, as they had hoped the president would do. Two senior administration officials bluntly predicted that firing anyone would be difficult now.

Many staff members describe an atmosphere of diminished morale in the White House, but they also insist that the news media frenzy surrounding daily disclosures about Mr. Trump is far out of proportion with reality.

Some have voiced hope that the appointment of a special counsel might even be a positive thing for the White House, because it could bring a resolution to a controversy that has hampered the president and stalled his agenda virtually since the day he took office. Mr. Trump and his top advisers have dismissed the accusations about Russian collusion as sour grapes from Democrats and an intelligence community that the president repeatedly criticized during the transition.