Give them a place to stay, with meals supplied. Soylant, peanut butter and jelly, occasional bologna. A 10x10 room with bunk beds and toilet in the corner. They can leave whenever they want, like if they get a job.
Your plan has got my vote!!
For that matter, we could cut the cost of our Congress, if we did the same thing for them! Pay them the same pay as our military members (equivalent with their years of service, of course), and a barracks with a common head! Those with families, would get their own private barracks housing (like the condos in Okinawa). A standard, military-grade chow hall!
See how fast they fix things, or get out of the games of politics.
This would encourage people who actually want to go to Washington and FIX problems, not those in it for the money, fame, sex, parties, and, did I mention the MONEY?!