On page 259 of his biography of Robert E. Lee, Allen C. Guelzo claims that after Antietam, there were rumors that McClellan approached Lee about combining their armies, marching on Washington, and staging a coup to overthrow Lincoln. Guelzo goes on to say that "Longstreet would later say that 'he was perfectly familiar with the McClellan letter incident'" and that "There had been rumors extending back to the Peninsula Campaign about unauthorized communications, under flags of truce, between McClellan's staff and the Confederate leadership."
Is there any evidence that this ever happened?
Ah, Guelzo...we meet again. The man isn't some quack armchair historian by any means, but to say that his scholarship is contentious would be an understatement. I got around to reading his biography on Lee a couple years ago after he came up a few times on this sub and my conclusions seem to align with the broader historical community:
Guelzo stretches thin evidence at best, and outright fabricates at worst. His main argument re: McClellan and a coup relies on old, second and third-hand testimony decades after the fact when it isn't leaning entirely on scuttlebutt from the period without any connection to reality. His work reaches quite a bit, and doesn't align with anything remotely concrete from the period.
Long-story short: there is no real evidence that McClellan ever seriously considered or acted upon any sort of coup attempt. I wrote about it a few years ago here:
There is a lot of primary evidence from the time (journals and letters) where people spoke about McClellan being a traitor...along with anyone else that might have been at odds with a person's moral or political views. Bruce Catton talks about this quite a bit in 'Mr. Lincoln's Army' - which is funny, because his book is something like 50 years older than Guelzo's, yet has a firmer grip on the history.