A $3B claim does not equal a $3B payment.
These things get settled.
Citigroup sued Wells Fargo for $60B for interfering it its takeover of Wachovia in 2008. Case settled for $100 million.
BP will never be able to pay the full amount. BP is already responsible for close to $40 billion in fines, cleanup costs, and settlements as a result of the oil spill in 2010, with an additional $16 billion due to the Clean Water Act. Personally, I am unsure why the company has not filed for reorganization much like Texaco did in the 1980's (Texaco, Inc. v. Pennzoil, Co.).
"Someone said it takes 30 years to be an instant success" - Gabriel Barbier-Mueller, CEO of Harwood International