Last Updated 8:27 p.m. ET
Engineers began pumping heavy drilling mud into the blown-out Gulf of Mexico oil well Tuesday in what they think is their best chance yet to reach the ultimate goal in a delicate process - snuffing one of the world's largest spills for good.
Special Section: Gulf Coast Oil Disaster
On Tuesday evening, a leader of the operation to plug up the blown-out oil well said the process is going well.
Wellsite leader Bobby Bolton said it's possible crews could finish the so-called "static kill" Tuesday after the process began around 3 p.m. Officials, though, have said it could take days.
The effort involves pumping mud and eventually cement down the broken wellhead to plug it up. Officials say they won't know whether it worked until they can finish a relief well nearby in the coming weeks.
Capt. Keith Schultz says he's "very confident we'll be able to kill this well."
Tests for the effort started a couple hours earlier as crews probed the broken well bore with an oil-like liquid to determine whether there were any obstructions in the well and to assess the pressure of the bore and the pump rates it could withstand.
Meanwhile, CBS News Correspondent Mark Strassmann reports from Calumet Island, La., that oil will wash ashore for weeks to come. With the well capped, BP has scaled back cleanup operations, so on one's been to that island to clean oil there even though BP knows about it and that it has been sitting there since Thursday.
As for the well, crews should know within hours whether the mud is pushing down the oil as envisioned. But engineers still won't know for more than a week whether the attempt achieved its goal because they have to wait for completion of an 18,000-foot relief well to reach the reservoir from the bottom.
"This is a really positive step forward," retired Coast Guard Adm. Thad Allen said earlier, calling it "good news in a time where that hasn't been very much good news, but it shouldn't be a cause for premature celebration."
Company officials earlier said the static kill alone - which involves slowly pumping the mud down lines running from ships a mile above - might be enough to plug the oil leak.
But the only surefire way to make certain the well is permanently plugged is to fill it from below with mud and cement, via the relief well, in a so-called "bottom kill," Allen said. The relief well is set for completion as early as Aug. 11.
The static kill could take days to complete, mostly because it involves slow pumping of mud, said Allen, the government's point man on the spill response.
The effort is meant as insurance for the crews that have spent months fighting the spill. The only thing that had been keeping the oil from blowing into the Gulf was an experimental cap that has held for more than two weeks but was never meant to be permanent.
Allen added earlier Tuesday that there "should be no ambiguity" that the primary relief well will be finished, regardless.
It's important to begin soon, he said, with the peak hurricane season just around the corner. Tropical Storm Colin formed far out in the Atlantic on Tuesday, but early forecasts put it on a track off the East Coast rather than the Gulf.
And while diagnostic tests show that the 75-ton cap that has bottled up the oil since mid-July is sound, the static kill should give scientists more confidence the well won't leak again, he said.
"The quicker we get this done, the quicker we can reduce the risk of some type of internal failure" of the massive cap, he said.
A federal task force said Monday that about 172 million gallons of oil made it into the Gulf between April and July 15, when the temporary cap contained all the oil.
BP Oil Well Gushed 12 Times Initial Estimates
The task force said about 206 million gallons actually gushed out of the well, but a fleet of boats and other efforts were able to contain more than 33 million. The 172 million gallons is on the high end of recent estimates that anywhere from 92 million to 184 million gallons had gushed into the sea.
Judging by the latest estimate, BP could be fined up to $5.4 billion under the Clean Water Act, or as much as $21 billion if it is found to have committed gross negligence or willful misconduct.
The high-end fine would drop to around $17.6 billion if the government credits BP for the oil it has recovered, while the low-end fine would be around $4.5 billion.
BP Could Face up to $21B in Oil Spill Fines
Any fines would be on top of the compensation BP has agreed to pay to thousands of people harmed by the spill. Under pressure from the White House, the company set up a $20 billion escrow fund to pay all claims, including environmental damages and state and local response costs.
The company began drilling a primary relief well May 2, 12 days after the Deepwater Horizon rig exploded and killed 11 workers, and a second backup well May 16. The first well is now only about 100 feet from the target.
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BP and federal officials have managed to contain large parts of the spill through skimmers, boom and chemical dispersants meant to break up the oil.
Federal regulators have come under fire from critics who say that BP was allowed to use excessive amounts of the dispersants, but government officials counter that they have helped dramatically cut the use of the chemicals since late May.
The Environmental Protection Agency released a study Monday concluding that when mixed with oil, chemical dispersants used to break up the crude in the Gulf are no more toxic to aquatic life than oil alone.
As businesses along the coast continued to clamor for relief from losses caused by the spill, BP said it created a special team to reduce paperwork and speed up payments to "businesspeople who are suffering."
On the oil-weary coast of Louisiana, a capped well , reports CBS News correspondent Mark Strassmann.
No one knows for certain the long-term environmental and economic damage from this spill. And on coastal Louisiana, the two are intertwined, Strassmann notes.
Commercial fishermen worry oil may tar the sea bed where shrimp, oysters and crab breed. Hotel and restaurant owners worry the real lasting stain of the spill is a stigma that will scare away tourists for years.
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