Mr. Corallo is a longtime conservative public relations operative who now serves as spokesman for the Trump lawyer Marc E. Kasowitz and a growing legal team charged with defending the president in a web of investigations. His posts are a rare instance of a Trump ally publicly venting criticism of a president who prizes loyalty and is known to be averse to dissent.

“Hey Mr. President, where’s all the ‘winning?’” Mr. Corallo wrote last month, appearing to compare Mr. Trump to Bill Clinton, who hailed from Arkansas, and his famous parsing of words. “Or, like the guy from AR, are you going to tell me it depends on the definition of ‘winning?’”

Mr. Corallo, who has deep experience in the combat of Washington scandals, including Mr. Clinton’s impeachment, is not an employee of the White House or the Trump administration. It would be simple to dismiss his comments on Twitter as the personal social media musings of a private citizen.

But Mr. Trump, who makes little distinction between his own personal and official utterances, often bristles at mild slights, even in an informal setting. And he is particularly protective of his elder daughter. The president has lamented privately to friends that he feels bad that his daughter has taken so many slings and arrows because of voter anger over his policies and his statements.

Similar criticism of the president has scotched jobs for other prospective administration officials in the past. Dozens of potential candidates were passed over or eliminated from Mr. Trump’s list for having spoken ill of him during the presidential campaign.