It should be noted that one o the first actions by the Union when troops began arriving in DC was to cross the Potomac and occupy Arlington to prevent the possibility for Confederates to place artillery on the opposite bank.

Starting under McClellan in the summer of 1861 DC became by war's one of the most heavily fortified places on Earth with over 40 miles of fortifications and hundreds of strong points and forts. So yes it was incredibly militarized, with units of mostly heavy artillery who spent most of the war in garrison duty until Grant called them duty as infantry to replace losses.

They were also tested in July 1864 when a force under Jubal Early tested them at Fort Stevens in an attempt to draw forces away from the Shenandoah Valley and Petersburg, but they were repulsed.

On another note, after shooting Lincoln, Booth actually was questioned by a sentry while attempting to cross the Navy Yard bridge but was allowed to continue on.

Lincoln and McClellan: The Troubled Partnership between a President and His General by John C. Waugh and Lincoln and His Generals by T. Harry Williams are both books I would recommend.