Real life people we know who work in government or in DC for organizations you would recognize:
Graduates of Dartmouth, Wellesley, Tulane, University of Maine, Rowan in NJ, Emory, UConn, Temple, Ohio State, Kent State, Marquette.
Two did summer month long internships with their state representatives, one in DC and the other in the state of residence. The others NEVER stepped foot in a government agency for an internship and did not attend college anywhere near DC.
I think you need to be a bit more broad minded in your thinking about colleges. You want your kid to get a great education, be a good thinker, be a good writer, be able to look at a broad range of perspectives impartially, be articulate and polite.
That all can happen at a huge variety of colleges. Huge.