This is not the first White House where that has happened, of course, but lessons from past experience suggest why it can be corrosive. Frustrated that he was not being fully informed during the early days of the scandal resulting from President Bill Clinton’s sexual relationship with Monica S. Lewinsky, Michael McCurry, then the White House press secretary, famously referred to his strategy as “telling the truth slowly.”

Indeed, much like Mr. McCurry, current White House officials are frustrated that they have not gotten a full accounting of the episode involving Mr. Porter either, with many of them angry at John F. Kelly, the chief of staff, and Donald F. McGahn II, the White House counsel. In individual conversations with reporters, some White House officials warn that the information they have just provided may not be true and that they themselves do not know.

Still, some Republicans said the shifting stories were not the main reason it has been hard for the White House to move on. Ari Fleischer, a White House press secretary under President George W. Bush, said a bigger factor was that the president’s team accepted Mr. Porter’s denials until photographs were published showing one of his ex-wives with a black eye.

And then, Mr. Fleischer noted, the president’s only public comments at first seemed sympathetic to Mr. Porter and included no concern for the accusers or an acknowledgment of the seriousness of domestic abuse. Only on Wednesday, a week after the story broke, did Mr. Trump personally condemn violence against women, and then sounded aggrieved that anyone would make an issue of the fact that he had not said anything about it until then.

“It wouldn’t have made this story go away,” Mr. Fleischer said of the White House failure to produce a clean and consistent explanation. “This story was launched because the president didn’t address the issue of domestic violence and the White House believed Rob Porter. If they had done everything else perfectly since then, it still would have been a similar controversy.”

Representative Elijah Cummings, Democrat of Maryland, the ranking Democrat on the House Oversight Committee, has pressed for months for a look at the process for White House security clearances. Representative Trey Gowdy, Republican of South Carolina and the committee chairman, said on Wednesday that the panel would investigate the White House handling of Mr. Porter’s case.

“This is an administration that has consistently not been truthful with the American people and so when you start going down that road where your leader goes, that is President Trump, then you are constantly trying to get your story straight,” said Mr. Cummings. “Every time they go down one road, either a story comes out in the newspapers or something happens that causes them to say, ‘Oh, we’ve got to change course.’ ”