Okay, some thoughts here.
1) Why is Lee surrendering vs. "total defeat"? Surrendering his whole army
is total defeat - he's going to fight like the Devil himself to prevent that.
2) Which will do a number on the AotP.
3) "huge Washington garrison"? Barring the heavy artillery regiments (which could be converted back to infantry the way Grant did in 1864), the Washington garrison has been stripped to below the minimum of safety to reinforce the Army of the Potomac.
4) Confederate troops: Not counting bits and pieces from the ANV - say, the 15th Virginia Cavalry Cavalry - which would be drawn to to whatever force is assembled, Richmond has the following:
http://ehistory.osu.edu/osu/sources/recordView.cfm?Content=045/1067 (Scroll back a couple pages to see what Ransom's division is made up of)
Call it 12,000 regular troops, plus Corse's brigade (1,100 men), and 2,400 Local Defense Troops, plus odds and ends.
5) Remember point #2? If the Army of the Potomac has 50,000 men, counting the useful elements of the reinforcements it would be getting quickly and allowing for units returning home, I would be impressed.
ps.
Of course, there's also something around 25,000 usable field troops in 4th and 7th Corps, and 8th Corps if kicked into motion can probably spare another couple divisions.
But all in all, unless Lee's army is completely killed/captured/incapacitated/deserted, its surviving pieces can fall back on Richmond and still be a tough nut to crack for a while. Obviously the Confederacy will lose faster than OTL, but not "by October".