I always thought it was “The Beltway”.
The Beltway is a highway...it would be Inside the Beltway.
The Beltway is a term for I-495, the circular route around DC and its inner suburbs. It does not refer to DC as a city since it encloses a huge area far beyond the borders of Washington, but "inside the Beltway" refers to all the people, companies, and agencies that are part of the federal government and its mindset.