Which one? Without the specific name of the property, others who may have had similar experiences can't really help you.
As a general proposition, DC properties are so chock full that by 1 AM, walking someone isn't that uncommon. It's a city where everyone (not quite) has some status or some corporate or event affiliation, so properties simply could care less.
Did you insist on checking for other closer properties. There are times when DC downtown may be close to sold out, but the Marriott chain has tons of properties in DC and there is nothing that limits the property (or you) to Marriott.
While it's outrageous, one thing to consider is a call directly to the FD on the afternoon/early evening of arrival to make it plain that you are not a no show.