Even if Mac’s 100000 had been forced against the James and forced to surrender to Lee’s 65000 survivors of the Seven Days, Lincoln could still count on Pope’s 40000 further North and the Washington garrison and various smaller detachments. The initiative would have been firmly in Lee’s hands, but defence was far easier than attack.
Possibly a European intervention would have occurred, but I try not to dwell on that possibility much. (I would rather stick to the battles and what happened.)
Lee’s march North would have required a few weeks to materialise and this time could have been used to transport Western troops East by rail. (They might even have ended up with Grant a little earlier!)
Lincoln would not have given up. He would have brought every man East if he could save his Capital and the Union.
I cannot, thetefore, see how a Cannae like battle, much dreamed of by Lee, would have brought about a Federal collapse.