Any chance you booked on a credit card with Trip Delay insurance? If with a Chase card with coverage, for example, you'd have $1500 (you + spouse + infant) budget which would cover at least a few nights of ORD Hilton without having to jump through airline hoops. Just pay in cash now and get reimbursed later. You would have to jump through insurance claim hoops, of course, but that can be done from the comfort of your laptop at a later date.