Declaring a "state of emergency" is just a technicality to free up the funds in accordance with the law. Sure there are a lot more homeless generally in D.C.; but the federal government didn't ship them here, so D.C. has to deal with them as an ordinary course of business just like every other city. The federal government bussed in these 300 and can't reasonably expect to demand that D.C. pay for everything. So the fast way to deal with the money issue is to comply with the letter of the law and use the money that's already there.