No, it shouldn't. DC is essentially a city, and there's a reason that cities aren't granted the same rights and representation that are granted to states.
To get an idea of why this is, we can look at texas's 13th congressional district:https://en.wikipedia.org/wiki/Texas%27s_13th_congressional_district
This district is pretty large, and has a population greater than a few states at 707,365. So why exactly is this place not getting two senators?
The fairly simple reason is that the district is very, very rural in nature, and is thus extremely monolithic politically. In each of the past four congressional elections in the district, the republican has won anywhere between 85 and 91 percent of the vote.
Which is the problem in a nutshell. Both cities and rural areas are essentially monolithic politically and have basically zero political diversity. Thus, to have a functioning state, you need to have both rural and urban areas to create a more moderate political environment.
Washington D.C specifically is a prime example of a lack of political diversity in cities and rural areas. In the entire 60 year history of DC having electoral votes, it has given them to a republican candidate a whopping zero times. And most of the time, the election there looks like this:https://en.wikipedia.org/wiki/United_States_presidential_election_in_the_District_of_Columbia,_2016
A much more appropriate solution IMO is to cede the land of the district back to maryland (the portion taken from virginia has already been returned) and only keep the parts directly around capital hill where no one lives as the federal district.
Edited 12/13/2016 00:30:25