You're right - Lt. Gen. Longstreet said Lee's "blood was up" and Lee made a terrible decision at Gettysburg. Had he won, the Union would have been forced to sue for peace. I also believe that had he broken off the fighting early and invaded Washington instead (there were no Union divisions left between Gettysburg and Washington), Lee would have been able to force the Union to sue for peace. In fact, that was Longstreet's recommendation, but Lee said the enemy was "here" (Gettysburg) and that is where he wanted to fight them.
Poor Brig Gen Pickett. In later years, he was a bitter man. The south blamed him, because they could not bring themselves to admit that Gen Lee would have blundered. Pickett used to say "that old man had my Division slaughtered." He had to live with it the rest of his life.
Lee knew he was living on borrowed time, and that his army had to make bold moves in order to achieve victory. He just went a bridge too far.
While there were no Union Army forces between lee’s Army and Washington, other than the Army of the Potomac, there were 95,000 Union soldiers manning 44 forts with over 500 big artillery pieces defending Washington. It is very doubtful lee could have forced the Lincoln administration to sue for peace. Longstreet did not council Lee to move on Washington. Longstreet recommended they break off action with the Army of the Potomac, move the army to a more defensible location and force the Union Army to attack them. This is the same advice that he gave to General Lee in late May before the Gettysburg campaign started. Lee at that time stated his plan was to find suitable ground in Pennsylvania and attack the Army of Potomac there.