There probably isn't a supply of bio-diesel in the capitol, so they'd have to chopper in the fuel. There is already an ample supply of Jet-A to fuel our hypothetical bio-diesel choppers due to the squadron of giant Marine One Sikorskys the president uses to fly to and from either of his 747s.
So yeah, a bio-diesel car could work among all those turbines, and it'll give the greentards another fine token to hang their hat on.
But since Washington D.C. already has an ample supply of electricity from its notoriously dirty 100+ year old coal burning power station, using a battery powered limo is probably the better choice. Then they can forgo the whole bio-diesel chopper supply thing and nothing says you love the "environment" quite like a genuine coal-powered car.