The catastrophic spill in the Gulf of Mexico set off a backlash against the oil industry yesterday, with a demand for a ban on future offshore drilling. The anger came as BP executives admitted in a private briefing for members of Congress that the gusher on the floor of the Gulf of Mexico could reach 40,000 barrels a day – eight times higher than the current estimate – if they cannot cap the flow.

It also carries the risk of a financial sting, with the White House yesterday backing a proposal by senators that would put oil companies on the hook for up to to $10bn (£6.5bn) for the cost of a spill.

The White House spokesman, Robert Gibbs, said the administration supported a proposal to make liability retroactive. The cap would be 133 times greater than the $75m bill that BP, which operated the Deepwater Horizon rig, faces under existing US laws following its explosion on 20 April. "It's time to believe our eyes and accept the obvious risks of drilling," Robert Menendez, a Democratic senator from New Jersey, told a press conference. "This is about making Big Oil responsible for its excesses."

Arnold Schwarzenegger, California's governor, had arrived at a similar conclusion, reversing his support for expanded drilling to help the state's $20bn budget crisis. "You turn on the TV and see this enormous disaster; you say to yourself, why would we want to take on that kind of risk?" he told a press conference.

The spill does not appear to have forced a change of heart for the former governor of Alaska, Sarah Palin, who popularised the Republican "drill, baby, drill" slogan in the 2008 election. She told an audience in Kansas City that offshore drilling should continue. "I want our country to be able to trust the oil industry."

But BP and other oil firms face further intense scrutiny in Congress. Company officials briefed members of Congress in a closed session yesterday afternoon, with a public grilling scheduled for next week.

BP's position that there had been no need for a backup system for the blowout preventer, whose failure led to the multiple spills, came in for harsh criticism yesterday afternoon. "I'm of the opinion that boosterism breeds complacency, and complacency breeds disaster," said Ed Markey, who helped write the climate bill which passed in the house last year. "That in my opinion is what happened."

The backlash against oil firms is dangerous for Barack Obama, who angered many Democrats and environmentalists in March when he announced a plan to expand offshore drilling, seen as a ploy to win support in the Senate and from oil firms, for climate and energy legislation.

But Bill Nelson, a Democratic senator from Florida, said that strategy would have to be abandoned. "I will make it short and to the point," Nelson told reporters. "The president's proposal for offshore drilling is dead on arrival." And in a new advert, with images of a burning rig and oil-encrusted wildlife, the liberal Moveon.org group asks: "President Obama, will you lead our country into a clean energy future? Or will we see more of this?"

The gulf explosion put the Obama administration on alert, scrambling to demonstrate full engagement with the spill, which threatens ecologically fragile areas from Louisiana through to Alabama and Mississippi and Florida, and could damage livelihoods of millions of people. After Obama's visit to Louisiana at the weekend, the White House said a number of cabinet officials would return to the gulf coastline this week.

The proposals unveiled by three senators yesterday would raise the legal cap on damages that oil firms must pay after a spill from $75m to $10bn. They would also do away with a $1bn per incident cap on an industry fund. The existing limits on liability are 20 years old, dating from the Exxon Valdez spill off Alaska.

However, those limits do not apply if it is found that BP was negligent or had violated government regulations at the time the Gulf of Mexico rig exploded.

Tony Hayward, BP's chief executive, refused to comment on the proposal yesterday. He has said the company will bear the costs of the clean-up and any "legitimate" claims arising from those who have lost their livelihoods. "We will absolutely be paying for the clean-up operation. There is no doubt about that. It's our responsibility‚ we accept it fully." He said the firm would also be prepared to pay individuals. "Where legitimate claims are made, we will be good for them."

But Menendez and others argue that $75m will not begin to pay for the lost livelihoods of shrimpers and others in the fisheries industries. "We're glad that the costs for the oil clean-up will be covered, but that's little consolation to the small businesses, fisheries, and local governments ," he said. Environmental activists are also looking closely at how to recover costs relating to the spill. To date, BP faces 20 lawsuits arising from the spill.

In Mississippi, attention has focused on the high number of sea turtles washed up dead along the state's beaches in the past three days. The Institute for Marine Mammal Studies in Gulfport has done necropsies on the turtles, but the first round found no visible traces of oil. A spokeswoman said more examinations were being done on tissue samples to see if there were hydrocarbons at a microscopic level.

Though experts have been struck by the large number of turtles, "at least 31 in latest counts", they point out that now is the season when the animals come close to shore and can get caught in fishing nets and suffocate. Moby Solangi, director of the institute, said the heightened degree of public alertness in the wake of the oil crisis might also explain why more dead turtles were reported this year.

BP said the oil slick was not expected to reach land for a few more days. "It's still offshore ... Right now we're not showing landfall for three days," its chief operating officer Doug Suttles said yesterday.