As others have pointed out: OTL examples exist. Of course, an ATL (additional and more influential) example can easily be created by having English and 'American' diverge considerably more than in OTL. There were tendencies towards this on both sides of the Atlantic, and it could be credibly argued that modern British English has actually diverged more from 'pre-split English' than American English has (although the verdict there does depend on which particular elements you pay most attention to). American English becoming 'estranged' is more likely than, say Canadian or Australian English deviating more extremely. Such alternatives are certainly possible, but less likely because those countries stayed with Britain for far longer, thus being more influenced by it. As such, the option to turn 'American' into a distinct language is easily the best bet, and using a scenario where (British) English also changes more than in OTL--but just in the "opposite direction"--maximises the potential for differences.
A possible ATL that could get you spectacular results is the famous "Jacobites in American exile" scenario. If this leads to a Catholic Anglo-American country that is estranged from (and likely hostile to) England, this country could be allied to France. The "Atlantic divide" with Britain keep the two very much apart, while the Anglo-Americans are influenced by their (also Catholic) Franco-American and Spanish-American neighbours. An "American" language eventually develops, which is more like historical English (it doesn't change along with the language in Britain, retaining its existing form by and large), but with the kind of random changes that just creep in over time, and strongly influenced by French and (to some degree) Spanish. At the same time, this scenario leads to stronger anti-French and anti-Catholic tendencies in Britain, and during the ATL age of nationalism, English is purposely formalised in a way that reduces Romance elements to a minimum. Additionally, the general evolution of the English language is simply different than the isolated "American" language.
By the present day, the two languages are totally distinct.
(Granted, the old "America goes with Franklin's alphabet and Webster's preferred spelling and take it from there, boys!"-POD would also suffice, but I think the above would get you a more extreme result.)