"The top kill is proceeding broadly in line with our plan. … Clearly I'm as anxious as everyone in America is to get this thing done," Tony Hayward said on "The Early Show" Friday.
Hayward said that "nothing has gone wrong so far," and the company's confidence "remains around 60 or 70 percent."
"But because this is completely untested and we're learning as we go, we'll need to recognize those facts, I'm afraid. I really wish it was different. I really do. But it's not."
Hayward said the first phase of the job - pumping heavy mud into the well - was completed Thursday. A second phase, pumping "loss control material into the blowout preventer to try and create a bridge … against which we could pump" was completed early Friday. Another round of mud-pumping was set to begin later on in the day.
"So what we've done is demonstrated that the technology, which has never been used a mile beneath the seabed, is working. We've learned a lot about the pressure in the blowout prevent and the pressure in the well and we're continuing to execute the program as planned. I believe it will be around 48 hours before we'll have clarity as to whether or not it has been successful," he said.
On Friday, Coast Guard Adm. Thad Allen said heavyweight mud was able to push down the oil and gas coming up at great force from underground, but it has not overwhelmed the gusher or stopped the flow.
If the efforts to plug the leak with mud work, Hayward said the company would seal the well with cement.
Five weeks into the disaster, which has dwarfed the 1989 Exxon Valdez spill to become the, BP and the White House have become targets of an increasingly frustrated public. A CBS News poll earlier this week found that 70 percent of Americans disapproved of BP's handling of the spill. Just 45 percent were satisfied with the Obama administration's actions.
On Thursday, President Obama addressed the criticism, stating that "" for the oil spill response.
Mr. Obama is scheduled to visit Louisiana Friday to assess the damage and response efforts.
For his part, Hayward echoed the president's statement and said his company is at fault for the catastrophe.
"I think it's self-evident that we … caused this. We've said all along that this is our responsibility. And we're taking it very seriously. We're throwing everything at this to try and do everything we can to eliminate the leak, to contain the oil on the surface, and to defend the shoreline. A cup of oil on the beach is failure as far as I'm concerned."
If the top kill fails, BP's next best hope for controlling even part of the leak is a tinier version of something that has already been tried: a steel containment box to cap the well. A 100-ton box lies junked on the ocean floor, abandoned by BP after ice-like crystals clogged it.
While BP officials say the smaller box shouldn't have that problem, it's clearly not their preferred method. It has been sitting in reserve on the seabed for more than a week while engineers first tried to siphon off oil through a mile-long tube.
That succeeded in collecting 924,000 gallons before crews took it out to allow room for the top kill attempt.
If the small box doesn't work, BP officials say they will go back to the tube, crossing their fingers that a relief well still weeks away from being drilled far enough to affect the leak will help stop the bleeding.
And even that's not a sure bet. Obama said Thursday that authorities insisted BP drill a second relief well as a back-up since such wells often miss their mark.
BP said in a regulatory filing Friday that it has spent $930 million so far responding to the ruptured well, including costs for cleanup and prevention work, drilling relief wells, and paying grants to Gulf states, damage claims and federal costs. BP says it's too early to quantify other potential costs and liabilities associated.
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