The answer to this question will vary somewhat depending on exactly when we are talking about. George Washington's popularity rose and fell several times over the course of his life.
During his early career as a military tactician, Washington was well respected by the colonial leadership in Virginia. Partly because of his family's position and partly due to his natural aptitude as a leader, Washington was appointed to the position of major in the Virginia militia at age twenty. The following year, he was made the special envoy on a mission to make peace with the Iroquois. By being granted so much responsibility at such a young age, it was clear that many people respected and trusted Washington.
He continued to receive important commissions during the French and Indian War, further showcasing how well he was esteemed by colonial leadership. However, his blunders at Fort Necessity earned him a number of influential critics, although Washington received praise for his displays of courage under fire. After the French and Indian War, Washington continued to hold the respect of his community as a successful gentleman farmer and war veteran.
It was this respect that earned him the commission of general of the Continental Army during the American Revolution. The delegates at the Continental Congress largely agreed that he was the best man for the job. When he first took control of the army outside of Boston, many New Englanders chaffed at having a Virginian in command. Many members of the militia also disagreed with his heavy-handed implementation of discipline. However, he soon became symbolic of the Patriot cause. Despite the many hardships that he and his army faced during the war, Washington was regularly lauded as a brilliant tactician and hero by the revolutionaries.
Washington was a reluctant president. By the time he took office, he dreaded such a position of power. This was actually seen as a virtue by those who had just fought to rid themselves of the rule of tyrants. However, over the course of Washington's two terms, his popularity diminished. He regularly found himself in the middle of political feuds. His attempts to be the peacemaker often failed to please anyone. His second term as president proved to be particularly negative. A peace treaty that his administration made with the British was very unpopular. Things got even worse when Washington was unable to prevent the Whiskey Rebellion or bring it to a satisfying resolution. When he left office in 1797, many were happy to see him go.