That legislation, sponsored by Sen. Robert Menendez, D-N.J., would remove the $75 million liability limit on oil spills. That bill would also retroactively remove the liability cap for BP and the Deepwater Horizon disaster.

The Senate bill includes provisions mandating improvements in oil spill contingency plans and enhancing the claims process.

The House's SPILL Act was sponsored by Rep. John Conyers, D-Mich., chairman of the House Judiciary Committee, and Rep. Charlie Melancon, D-La.

It amends the wrongful death claims falling under the Jones Act to provide the noneconomic damages of loss of care, comfort and companionship to surviving family members from seamen's employers.

The House bill would also update several other outdated maritime liability laws that significantly restrict the accountability of Transocean by repealing the Limitation of Liability Act, an antiquated 1851 law that allows Transocean to claim it is only responsible for $27 million in damages–the current worth of its now-destroyed rig–despite receiving over $400 million from its insurance company.

Anthony Tarricone, president of the American Association for Justice, issued a statement noting, "The House's quick passage of this bill shows how current maritime laws desperately need to be updated if the negligent corporations responsible for the tragedy are to be held accountable."

He added, "The families of workers who died aboard the Deepwater Horizon, as well as those affected by other maritime disasters, are now one large step closer to receiving justice."

Congress is taking an Independence Day recess this week. It returns to work starting July 12.