Well first of all there was the Army of the Potomac, the largest and best supplied Union army. It normally sat between the Confederates and DC. And was no small obstacle.

Second, there was generally several corps sized bodies of men sitting in DC at any single point in time. So if the confederates ever beat the Army of the Potomac, it would have a nearly as large army still facing it. DC was the primary staging base in the East, in addition to being the political capital. There were generally upwards of 40,000 men resting, refitting, training, and most especially standing in forts.

Which brings us to the third major reason, it was by the end of 1861 perhaps the most heavily fortified city in the world. By the end of the war these had been extended further, "Fort Washington" had 37 miles of fortifications including 68 forts and innumerable redoubts and an additional 20 miles of pits and trenches for riflemen. It also had over 1,500 emplaced canons. DC itself was an almost impossible nut to crack.

Maryland was also heavily garrisoned along the railroads and at specific important points such as Baltimore and Annapolis. This wasn't sufficient to stop an army, or maybe even raiders, but it was more than enough against any potential civil disobedience.

There was one late scare in July 1864 when Jubal Early made a raid and play at the city. Discounting the possibility of an attack the city had fallen to about 31,000 troops, any only about 10,000 of them were deemed fit for battle. But Early only had 10,000 himself and in the end declined to assault the fort he found himself facing. Grant quickly sent two corps back to Washington, and faced with the idea of assaulting a fortified army that significantly outnumbered him, Early retired back to Virginia.

An equally valid question could be asked - how did Lincoln manage to not be assassinated until 1865? He would often go about Washington D.C. without even a bodyguard. Washington D.C. at the time was apparently full of Southern sympathizers, spies, etc.