BP is facing a bill of up to $34bn from the Gulf of Mexico disaster after US senators demanded the oil company deposited $20bn into a ring-fenced account to meet escalating compensation costs.

The sum dwarfs many analysts' previous estimates, shared by BP, that put the cost of the clean-up effort and payment of damages to affected communities, such as fishermen, closer to a total of $5bn.

Shares in BP nose-dived by more than 9% today as investors took fright at the demand by the 54 Democratic senators, who represent a majority in the US upper house. The company is now worth almost half what it was before the accident of just under two months ago.

BP already faces up to $14bn in civil penalties, payable under US environmental law, assuming the leak is plugged in August. These punitive damages are directly linked to the size of the spill – already estimated at being up to eight times worse than the Exxon Valdez disaster in 1989 – with BP liable for up to $4,300 for each barrel-worth spilt.

Senate leaders insisted the $20bn ring-fenced account should be exclusively for "payment of economic damages and clean-up costs" and should not be seen as a cap on BP's other legal liabilities. With punitive damages pending too, the theoretical total of $34bn is equivalent to more than half the corporation tax paid by all British companies last year.

Tony Hayward, chief executive of BP, and other directors of the company, will meet Barack Obama at the White House on Wednesday prepared to offer concessions in the hope of taking the sting out of mounting political attacks on the company.

BP will be in "listening mode", willing to cut its next dividend, worth about $2.5bn, possibly paying the cash into the clean-up fund. It will also reiterate its commitment to paying all legitimate claims arising from the disaster. But the company does not believe that the demand by the senators to stump up $20bn is justified.

Executives were also alarmed by the White House's insistence last week that BP must pay the wages of rig workers laid off by other firms because of the six-month moratorium on deepwater drilling in the gulf. If pursued, the company fears it would be exposed to potentially limitless claims from anyone affected by the disaster, which would eventually bankrupt the company. The company hopes that President Obama's statement, following the meeting with BP, will draw back from the demand.

Hayward, who was in Houston today overseeing the spill response, hosted a conference call with his board to discuss BP's next move. The company had indicated that it would wait as usual until close to its next results announcement, on 27 July, to decide whether or not to pay its next quarterly dividend. But it is now set to announce its intentions sooner, perhaps as early as Thursday. It is understood BP could use the dividend as a bargaining chip in its talks with the White House.

Obama today risked the wrath of families of 9/11 victims by comparing the gulf spill to the 2001 terrorist attacks, as pressure intensified on the White House to show greater urgency over the crisis.

Ahead of a trip to Louisiana and a televised address to the nation tomorrow, Obama said the spill, the worst environmental disaster in US history, would, like the 2001 terror plots, continue to influence the country for decades to come. Some people who lost relatives in the 9/11 attacks rejected the comparison. "I think he's off-base," said Jim Riches, a former New York fire department deputy chief, whose son died at the World Trade Centre. "These were 9/11 murders … not something caused by people trying to make money."