an alternate path:
Washington goes down. those around him are horrified. rather than rally around the fallen, Washington's troops join the fleeing. At the end of the day, it's not a complete rout, but it halts the string of victories the Patriots had put together.
(OTL, Washingtons rally of the troops fosters a spirit of confidence. closet patriots start coming out of the closet. TTL, they stay in the closet. Loyalists start peeking out thinking that maybe the mother country will prevail)
Greene takes over temporarily, but ultimately Congress decides to go with a veteran, who just happens to have some political backing - Gates.
(OTL, Washington had a real appreciation of the danger of smallpox and took a lot of precautions to minimize it, and called for the variolation of all new troops. ATL, Gates doesn't take such precautions)
(OTL, Howe tried to draw Washington into a battle in New Jersey in the spring of 1777. Washington didn't bite. Gates, though, in an effort to cement his hold on the military gets sucked in)
Gates suffers a moderate loss in New Jersey.
Howe moves on to Philadelphia. Gates throws all his resources to prevent this. this means that troops that OTL were sent to NY to oppose Burgoyne (including Benedict Arnold) aren't sent. Gates, supports his cronies. Guys who won't challenge his spot at the top.
Burgoyne, despite all his bungling ways, accomplishes his mission. Saratoga is a close run thing, but, sans the support OTL Washington sent, with questionable Patriot support, and Loyalists coming out of the woodwork, British forces prevail. Bottom line: by the end of 1777, the Hudson Valley is in British hands. Control is tenuous, but NY Loyalists are increasingly encouraged to blast back at the thug Patriots who have been bullying them into submission.
Philadelphia falls. Gates is having trouble getting material support from Congress. Smallpox keeps popping up, killing his troops at a rate that rivals enemy fire. Morale in the troops is waning.
Winter Quarters is a harsh environment for the Patriots. The French have backed off what seemed, only months before, sure support. The French and Spanish are willing to send a little bit of clandestine life support, but no more. Close quarters brings on a smallpox epidemic. lack of support from Congress means there's more bloody footprints in the snow than OTL. A capable officer named Stueben is shuffled to the side in favor of a dundering crony of Gates. Sanitation woes and discipline are major problems. More and more troops say 'screw this' and leave to try to make their way home.
Britain has sent a delegation to try and work things out. (OTL, they are dismissed out of hand, because the Patriots know they have France coming to town, and because they are increasingly winning battles). The colonies are starting to waver. '76 was a good year. '77 was supposed to build on it. but '77 turned out to be a dud. Worse than a dud. no wins. a couple of losses. a couple of draws. Not the kind of year to enthuse the populace to support the cause.
"How about limited home rule?" says Britain.
"No dice" says the Patriots.
1778: The Patriots are having a hard time recruiting. Loyalists are increasingly seeing which way the wind blows. Borderline Patriots are hedging their bets and going Loyalist, or at least remaining neutral. Britain has severed the colonies. Massachusetts is still firmly rebellious. But NY/Pennsylvania is now Loyalist country. Vermont is pretending to be independent, but making overatures to British Canada. Virginia is rebellious, but the further south you go, the more iffy the cause is. British plans center around keeping the northeast isolated while crushing the south. Gates is in trouble. Congress is tired of his losing ways. He can't hold an army together. the 'country' is now separated. But, he's managed a few draws, and politics (which OTL is spoke of so glowingly) lets the Patriots down, so he's given another chance. but he's on a short leash. He doesn't get the support he needs, so predictions of failure become a self fulfilling prophecy.
British adopt a strategy of subduing the south. Ultraloyalist Florida troops move north. Free to move their troops around at will, the British make gain after gain. Holding down the fort in NY, the British move their army south to Virginia. Gates wants to adopt a strategy of defense, but his tenuous position means he must be aggressive to bring the French back into the fold. His attempt leads to a major defeat. a total eclipse of the sun is taken as a sign of doom for the embattled patriots. more and more, desertions decimate the state militias, the last hope of the Patriots. by the end of the year, things look grim for the rebels. Gates has finally been replaced by someone more competent, but it's too late. the tide has turned.
The British peace commission, realizing that a compromise must be reached, offers again limited self rule. The political overlords in Britain are starting to think that they don't need to be generous, but communication is slow. Plus, there's opposition to continuing spending money on the colonies. overall, an air of compromise is taking place. Both sides are exhausted. Britain is realizing that they need to give a little. the Patriots are realizing that full independence is a pipe dream. The middle colonies and the southern colonies are, in various states of willingness, ready to sign off. Massachusetts is a problem, though. It's independence or bust for them. So the whole confederation breaks down. by 1779, only the northeast is in rebellion. by 1780, peace is fully ensconced everywhere but the northeast. Britain has adopted a policy of slowly squeezing the last of the rebels. Easily blockading the last of the rebellious coast, the rebels are in a world of hurt. the Brits send their armies against the rebels, but are cautious to not put themselves in a position of possibly losing a battle. Britain isn't spending anywhere as near as much as they previously were on prosecuting the war, but they still are spending too much. As the months pass, both sides are becoming more urgent to find a solution. Finally, at long last, the northeast is established as a full self rule region. this causes some friction within the colonies. some are jealous, and kicking themselves that they didn't hold out for more. Some are happy that they don't need to worry about protection from the indians. The Northeast still isn't happy, but the die has been cast. these united states aren't going to be so united. there are wounds that are going to fester. the northeast isn't going to trust the south. the south is mad at the Northeast. Virginia is pissed because the Vandalia is established as a new colony. Britain has declared the Northwest territory to be Indian country, but bows to reality and lets Ohio, Kentucky, Tennessee be settled. There's plenty of room for expansion, which lets the steam out of the kettle for several decades. Florida grows and pushes north. the Indian country of the south is squeezed.
France doesn't have the massive debt from supporting the revolution. The crisis years of late 80's, early 90's are eased a bit. Instead of supporting the revolution, France firmly said no to Austrian expansion into Bavaria. As OTL, Austria backed down. The debt load is a tough weight to bear, but without being overwhelming, the perfect storm which lead to the French revolution is reduced to a rough storm which is ridden out. Tough times, for sure, but no reign of terror, no Napoleon. At the end of the day, there emerged a weak monarchy, with some sort of congress helping keep monarchy in check.
The patriots had hoped for a European war to sidetrack the Brits while they went for round two of the rebellion. Sadly, it didn't happen, and a new generation came of age, one which accepted British protection with significant self rule. And then another generation. and another. There were Indian countries, one north, one south, but slow encroachment allowed population release from the coast. Spanish Louisiana slowly grew. Spain didn't dare block access up the Mississippi, with British control of everything east, so there was no issue of transport of goods. some colonists made their way west of the Mississippi, but willingly traded one king for another. Made no difference to them as long as the overlords let them have their space, which was a given, considering the distances involved. The Brits and the Spanish provided protection against the indians, which allowed the settlers to settle. The British wanted to go coast to coast, but Mississippi and all points west and north was a pretty good chunk of land, and there was no real danger of Spanish trying to expand (they were lucky to hold on to the territory they had), so no real need to engage in war to dispel the Spanish. The Brits, although legally not allowed to trade west of the Mississippi, didn't much care for legalities. the smuggling business was good. why rock the boat?
Slowly, surely, time marched on. No master can hold on to their student forever. Eventually, the eastern colonies gained independence. three countries: northeast, middle, and south. Mexico split in two: the conservative mexico proper, and the European influenced north and Louisiana. Oregon country went to Canada. The Northwest Territory went to Canada.
And this notion that there was one grand republic stretching from sea to sea was merely a footnote left bleeding out from the neck of George Washington, whose last thought was not of his beloved Martha or of an independent country, but 'oh damn, this hurts'.