It is amazing to see how US president can effectively demand something of a private company. No courts needed anymore.
Agreeing to a payment system now, ahead of sorting out the exact fines, is a PR win for both BP and Obama.
if popular opinion wasn't so strongly against BP, the president's demands would have been meaningless, so this isn't about the president and his "powers," but about the kinds of things you have to do when everyone is rightfully pissed at your company
Also, even if the administration did hypothetically agree this was a cap it would likely not be binding on the courts without further Congressional action when people brought the lawsuits.
$20bn seems like a lot for PR, why wouldn't you fight that? Unless there is some sort of cap or some reason. What about the folks taking the pay outs too? I'm sure there is some paperwork to sign before you get a cheque.
Looking at like the Iraq reconstruction funds, I expect that $20bn to be spent in about a month, a lot of folks won't be paid, we won't know where the money goes and it's just going to be gone.