Not quite, Washington DC was one of the most heavily defended cities on the planet at the time. It was ringed with over 50 forts, with 800 cannon, with 20 miles of rifle trenches and hundreds of battery emplacements. Nearly 40,000 men manned these works. this large concentration of troops in Capitol meant that these men were not available to reinforce Army of the Potomac as it marched north. General Hooker resigned as the AOPs commander because Washington would not release any of the garrison to the AOP.
Actually, Hooker “resigned” over the Harpers Ferry garrison.
Washington’s defenses were second to those at Richmond, built by slave labor and at the direction of RE Lee.