The $20B that BP has agreed to put into an escrow accound will be funded over 2 or 3 years. Since BP was paying about $9B (3.3 billion shares at $3.36/share) they will be able to fund it just from suspending their dividend. Especially since the dividend funds have already been taxed and the costs will be deducted from their US income taxes as the money is spent.
Over the years, I have dealt with BP a few times and they are not dummies (except in cost cutting while drilling wells in deep water).
They operated many offshore fields in the North Sea as well as the Amoco properties they acquired in the gulf.
If political noise could stop the oil flow, it would have been stopped a couple of months ago.
I think their problem is the current ongoing costs and whether they are a part of the $20B or not.