Very true. And even after proving himself, as late as 1783 he faced another potential overthrow related to the Newburgh Conspiracy. In short, the government didn’t have the funds to pay all of the active soldiers for their service. In a play for power a small group of folks were inciting all sorts of actions from protest, to physically demanding payment from Congress, to oust George Washington, and even potentially establish military rule. The extent of these “plans” is not fully confirmed as one could consider 2 century old back room dealing conversations to have little documentary evidence, yet it was presumed Horatio Gates was involved yet again in some capacity to oust Washington.
More related to your point of Washington saving situations in just the knack of time, when tempers were flaring and a meeting of high-ranking army officers was called to determine a plan of action to get payment, Washington made a surprise visit to the hostile crowd and with one sentence, he eloquently ingratiated himself with all that were present. Before starting his speech, he spoke:
“Gentlemen, you will permit me to put on my spectacles, for I have not only grown gray but almost blind in the service of my country.”
With that one, powerful sentiment, many negative thoughts dissipated and the respect many of the officers once had, returned. This lessened hostilities and was a point from which more peaceful means were determined to address the overall situation/”conspiracy”. Washington’s subtle, yet strong and influential leadership (albeit very calculated), once again helped unify.