Early set backs suffered by the Continental Army, especially the string of defeats suffered by Washington in 1776-7, led more to a questioning of Washington's leadership than to discussion of surrender. By the winter of 1777-8, Washington had lost New York City and Philadelphia, and suffered defeats at Brandywine and Germantown. Other than Trenton and Princeton, Continental forces under Washington enjoyed no clear victories over British forces. Washington's failures stood in stark comparison with Gen. Horatio Gates' defeat of Gen. Burgoyne's invading Army at the Battle's of Saratoga.

Not only did Gen. Gates defeat a large British force head-to-head in pitched battle, something Gen. Washington failed to do. But this victory also influenced France to join the war on the American side, something Gen. Washington had failed to do through his own conduct on the battlefield.

Following Washington's failures and Gates successes throughout 1777, Washington received criticism, most of it in private, from members of congress, the army and other influential Americans. Benjamin Rush, James Lovell, John Adams, Samuel Adams, Jonathan Sergeant, and Abraham Clark complained that Washington deferred too much to subordinates such as Nathanael Greene and Alexander Hamilton, and relied too much on formalities and general orders. Those within the Continental Army also questioned Washington's leadership, with one Lieutenant stating "'let Gates,' say they,' take command, and we shall see an end of the war'". Gates himself sent reports of his victory at Saratoga directly to the Continental Congress, instead of to Washington, his senior officer. This Washington perceived as an affront.

Following Saratoga, Congress appointed Gates to be president of the Board of War, and appointed Gen. Thomas Conway to be Inspector General. When a letter written by Gen. Conway to Gen. Gates in which Conway derided Washington's leadership and expressed his desire for Gates to be Commander-in-Chief was intercepted by an officer loyal to Washington became public, rumors of a cabal exploded. In January 1778, letters by Rush to Patrick Henry and John Adams, criticizing Washington and praising Gates reached Washington. In February 1778, the Boston Gazette published an anonymous letter praising Gates.

However, even amongst Washington's harshest critics it was clear that there was no real plan in place to attempt to replace Washington with Gates. The talk had never materialized into action. Ultimately, the inaction of the "cabal" and Conway's being wounded in a duel to protect Washington's honor solidified Washington's position as Commander-in-Chief.

You can read more about the Cabal here in a post by u/Kent_Woolworth about why Thaddeus Kosciuszko wasn't included in "Hamilton".

Royster, Charles. A Revolutionary People at War: The Continental Army & American Character, 1775-1783. The University of North Carolina Press, 1979

Sorry, follow up question, Why does George Washington have the status of a great military commander who won the revolutionary war when it seems like that was not the case?