Sure, Lee's army did have to cross a river. But, before they were able to, they realized they were going to have to wait awhile, so what did they do? They dug in behind fixed fortifications. Anyone ever remember hearing of a battle in Virginia in Dec. of 1862 involving a dug in army and fixed fortifications? I do.
Take any army of 90,000 men with a new commander. March it many miles in several days. Let it fight brutally for three days, losing 25% of its effective strength, including three of its corps commanders, two of whom were most excellent. Also, take from it several brigade and division commanders, and dozens of regimental commanders. Through in a severe rain, and then expect the exhausted and most likely battle-fatigued men to mount a pursuit against an army that they've finally beaten, led by a commander with a reputation of snatching victory from seeming defeat and defying the odds time and time again. Better to wish upon a falling star, because at least that does not spell out the recipe for disaster.