Not even plausible as a "what-if" scenario. Attacking Washington would have meant assaulting a heavily fortified series of fixed entrenchments, an undertaking for which Lee and the ANV was not prepared to do.
According to the Alliance to Preserve the Civil War Defenses of Washington:
"Union officials began to fortify the capital and its treasury against the feared invasion. By the end of the Civil War, the city was the most heavily fortified city in the world, bristling with 68 forts and artillery emplacements, more than 1,000 guns and mortars, and 20 miles of connecting roads, trench lines, and rifle pits. Constructing the Defenses of Washington was the greatest engineering project of the war. Under the direction of the army's chief engineer, Colonel John G. Barnard, thousands of soldiers and civilian workers labored throughout the war to turn rural farm fields, orchards, and woodlands into an imposing system of connected defensive fortifications."