Sen Bill Nelson, D-FL, just told reporters that NOAA has informed members that the oil in the Gulf, following the BP rig explosion, is expected to reach land Wednesday with the prevailing winds. "The question then is, which way does it go."

Nelson then spent about 40 minutes with executives from BP, who requested the meeting.  BP's CEO Tony Hayward, along with the chairman of BP America, Lamar McKay, attended.

Afterward, Hayward told reporters, "We are throwing all of the resources at our disposal at it."  Hayward said his teams will try, by the weekend, to to plug the hole in the pipeline that is gushing about 200,000 gallons of oil per day, but Hayward warned that there could be problems.  

"The Dome will go in place on Thursday. We will be hooking it up over the course of the weekend. This has never been deployed. It's a technique the industry uses often in shallow water...It has never been deployed at 5,ooo feet, so we should not expect that it will go perfectly."

When asked if BP would go above and beyond the $75 million liability cap on economic damages incurred by fishermen and others from the spill, Hayward said his company would "honor all legitimate claims," adding, "I think it is inevitable that the (economic damages) cap will be exceeded."

But Nelson says when he pressed Hayward about economic damages in their closed meeting, specifically, Hayward would only say that this is something that will be worked out in the future. When a reporter asked, "You got the sense he would fight it?"

"Oh yea," Nelson said. The senator says he told Hayward that Transocean, which built the shut off valves, should be liable. Hayward responded positively, Nelson said.

Nelson said he would consider offering an amendment to the financial reform bill on the Senate floor that would increase the economic damages cap to $10 billion, but a senior Dem leadership aide tells Fox that is not likely, given the abbreviated schedule in which the regulatory bill will be considered.

Hayward, according to Nelson, spoke of how how  all 3 layers of security shut offs failed after the explosion. He said there is evidence the shut off switch was flipped. The pressurized system known as "dead man" also failed. And the 3rd safety mechanism, the robotic devices on the sea floor were supposed to pump metal plates to shut off the pipe. Hayward said they kept trying this 3rd option, but the metal plates were not shutting.

"This potential economic and environmental disaster could be of epidemic proportions," Nelson said.

Nelson, for his part, praised the Obama Admin's response to the spill but condemned Minerals Management Service, which is responsible for the nation's resources in the Outer Continental Shelf, under the Bush Administration as "too cozy with big oil," reminding reporters of sex and pot parties back then.

He said he hopes the Obama team is "kickin some butts" at MMS.

Nelson, long an opponent of drilling off the coast of Florida, said he thinks the mood has decidedly shifted in the Senate against OCS drilling. When asked if OCS drilling is no longer inevitable, he said, "Well, of course."

He recounted going up to some senators and repeating a 2008 GOP campaign mantra, "Drill baby drill?" to which he says those GOP senators "rolled their eyes in mock horror."

Hayward and McKay also met Tuesday with GOP Sens. Thad Cochran and Roger Wicker of Mississippi, George LeMieux of Florida, and spoke by phone w/ David Vitter of Louisiana, who was in the region monitoring the spill cleanup.