NEW ORLEANS – BP mounted a more aggressive response to the oil spill in the Gulf of Mexico on Sunday as it deployed undersea sensors to better measure the ferocious flow of crude while drawing up new plans to meet a government demand that it speed up the containment effort ahead of President Obama’s visit to the coast.

The financial ramifications of the disaster are growing by the day as the White House and states put pressure on BP to set aside billions of dollars to pay spill-related claims in a move that could quickly drain the company’s cash reserves and hasten its path toward possible bankruptcy.

BP was also trying to meet a Sunday deadline to respond to a letter from the Coast Guard demanding that the British oil giant intensify the efforts to stop the spill. One of the actions BP took Sunday was to use robotic submarines to position sensors inside the well to gauge how much oil is spilling.

The robots were expected to insert the pressure sensors through a line used to inject methanol — an antifreeze meant to prevent the buildup of icelike slush — into a containment cap seated over the ruptured pipe, BP spokesman David Nicholas said.

BP was installing the sensors at the request of a federal team of scientists tasked with estimating the flow, Nicholas said. He did not know when the request was made.

Scientists haven’t been able to pin down just how much oil is leaking into the Gulf, although the high-end estimates indicated the spill could exceed 100 million gallons. The government has stressed that the larger estimates were still preliminary and considered a worse-case scenario.

The Obama administration’s point man on the oil spill, Adm. Thad Allen, on Sunday said government officials think the best figures are from a middle-of-the-road estimate, which would put the spill at around 66 million gallons of oil. That is about six times the size of the Exxon Valdez spill.

BP is currently capturing about 630,000 gallons of oil a day, but hundreds thousands more are still escaping into the Gulf. The company has said that it could begin siphoning an additional 400,000 gallons a day starting Tuesday by burning it using a specialized boom being installed on a rig — and any new success would be welcome news for Obama as he returns to the Gulf.

The president was scheduled to arrive in the Gulf today for a two-day visit that will be followed by a nationally televised address to the American people Tuesday and a sit-down with BP executives Wednesday.

The crisis has already become a crucial test for the Obama presidency as it takes a greater toll on his image with each day that more oil gushes into the sea.

“We’re at a kind of inflection point in this saga, because we now know that, what essentially what we can do and what we can’t do, in terms of collecting oil, and what lies ahead in the next few months,” senior adviser David Axelrod said on NBC’s “Meet the Press. “And he wants to lay out the steps that we’re going to take from here to get through this, through this crisis.”

Obama wants an independent, third party to administer an escrow account paid for by BP to compensate those with “legitimate” claims for damages. The amount of money set aside will be discussed during talks this week between the White House and BP, but the request will most definitely be in the billions.

Louisiana’s treasurer has said that it wants $5 billion. Florida said it wants $2.5 billion.

“We are aware of the request,” said BP spokeswoman Sheila Williams in London. She declined to comment further.

BP could have to tap its cash reserve to pay the fund while also borrow money to comply. That, however, presents a potential problem because the company’s borrowing costs are likely to be a lot higher because of investor concerns.