An escrow account. Washington Post:

President Obama will demand that BP establish an escrow account to compensate for Gulf Coast oil spill claims when he meets with company executives on Wednesday, White House officials said Sunday.
Obama is expected to announce the details of the escrow account request during an address to the nation Tuesday night, which he will make upon returning to the White House after a two-day trip to the region, senior adviser David Axelrod said.
“We want to make sure that money is escrowed for the legitimate claims,” Axelrod said on NBC’s Meet the Press. The president’s discussion with BP executives will focus on the amount of money that should be set aside in the account, an amount Axelrod said should be “substantial.”
Coast Guard Adm. Thad Allen, the government’s top point man on the oil spill response, said Sunday that the administration may appoint a third party official to oversee the fund and ensure payments are made quickly.
“We’ve been very concerned about the claims process,” Allen said on CBS’s Face the Nation. “This is not a core function of an oil producing company.”
BP spokeswoman Anne Kolton said “We are engaged in ongoing discussions about the best way forward. We look forward to meeting with the administration later this week to affirm our commitment to fulfill our obligations in dealing with the tremendous impact of this tragic incident.”

The rest here. Unanswered is who will decide how and when claims are paid and for what. There’s no way BP is going to agree to an ATM machine that BP has no control over.