As the $7.8 billion settlement of the massive litigation over the Deepwater Horizon oil spill heads toward final approval, BP PLC and Anadarko Petroleum Corp., both of which leased the drilling site at the heart of the case, face additional billions of dollars in liability to the federal government.

The settlement, announced on March 3, would resolve claims by thousands of individuals and business owners against BP. The last day to object to the deal was August 31, and the deadline to opt out is November 1. A final settlement hearing is scheduled for November 8.