So originally U.S. Grant and his wife were to accompany President Lincoln and Mary Lincoln to Ford's Theater. He, obviously, couldn't go. During the assassination, Major Rathbone was injured by Booth's hunting knife. Lets say Grant goes, and during the brief struggle right after shooting the President Booth manages to sink his knife into Grant's neck or other vulnerable place, leading the general to die as well.
How does this change things from this point forward? Can men like Sherman, Thomas and Sheridan do well enough without Grant post-War? Any likely contenders for president in Grant's stead?