PolitiFact checked this statement from Brazile:

“Well, the administration has been constrained by the Oil Pollution Act of 1990, which basically gives the responsible party the lead role in trying to not only fix the problem, but contain the problem,” Brazile responded. “That has been the problem from day one. They’ve waited for BP to come up with the answers, and we know that BP continues to mislead people.”

Survey says: FALSE, with a tip-of-the-hat to Newsbusters.

We asked Brazile, a native of New Orleans who still has family living there, if there was something we were missing.
Brazile said she was trying to point out that the Oil Pollution Act, and the options the president had, may have contributed to the federal government not taking the lead sooner. “The Administration had every reason to take the lead and not wait,” Brazile said. “Perhaps they waited — and I used the reference to the Act — as one reason why they did not take the initial lead.” Brazill also suggested her statement — which was criticized by the conservative website Newsbusters — was being used to score political points in the middle of a national crisis. Her first concern, she said, is that people in the Gulf states suffering get help.
But in this case, her interpretation of the Oil Pollution Act of 1990, is incorrect. She said the law “basically gives the responsible party the lead role in trying to not only fix the problem, but contain the problem.” In fact, the Oil Pollution Act specifcially gives the federal government the authority to decide who’s in charge of the clean-up — the polluter or the government. The company, in this case BP, will pay for the clean-up response. But the federal government can give the orders if it chooses. We rate Brazile’s statement False.