Credibility gap

The inability of Trump's own spokespeople to speak authoritatively on the president's thinking and actions -- a challenge even Trump himself has acknowledged -- has left the White House with an enormous credibility gap, and has tarnished the reputations of many of its most visible spokespeople.

Source: wiktionary

The League of Nations, meanwhile, suffered a credibility gap as the United States never joined the organisation that its President argued was essential for preserving the hard-won peace.

Source: wiktionary