Hayward said plans for relief wells are on target for August, and he responded to fears that a hurricane in the interim could force BP to abandon containment efforts.
"At the end of the month, we will introduce more permanent containment/production systems that will be fully sealed, which will be better able to deal with hurricanes," he said.
The cut-and-cap strategy is BP's seventh attempt at controlling the leak. Since it began the operation Tuesday, oil has been gushing out an estimated 800,000 gallons per day, which is 20 percent faster than previously.
Oil has hit at least 125 miles of the Gulf Coast. A slick sheen is just four miles from the Florida coast today, the Coast Guard said. Just yesterday, it was nine miles away from shore.
Allen said the Coast Guard has deployed resources to the Gulf Coast beaches and the "picket line" has been established.
"We are flying more boom back into Alabama this morning, and we have dispatched a group of Coast Guard cutters with skimming capabilities that are down there," Allen said. "We've got helicopters offshore that are doing surveillance, Coast Guard patrol boats we are using for command and control, working with vessels of opportunity. These are local fishermen we have brought on board to help us."
Along the coast, there has been some concern about the health of those fishermen. ABC's Chris Cuomo, who was in the Gulf just yesterday, heard firsthand that many of the fishermen getting sick are too scared to report their illnesses out of fear that they will be fired by BP.
Today, Cuomo set out to answer that question, asking directly -- would BP promise not to fire people who report illnesses? For most of the day the company did not provide a clear answer.
But after hours of reaching out to Unified Command, the Coast Guard and the White House, BP finally came forward with a statement late today which said "workers with health issues are encouraged to report their conditions without fear of reprisal."
There have been calls for a drastic response to the oil leak, some even suggesting a nuclear explosion to stop the blowout.
"The only technology we've ever had to deal with blowouts very severe is -- a very small-scale nuclear device -- right on top of the oil column, [detonating it] to en capsulate the stuff because it turns the earth into glass," said Matthew Simmons, an energy expert.
Both BP and officials in Washington said a controlled nuclear blast is not on the table.
"That hasn't been seriously briefed to me," Allen told "Good Morning America." "I think we have to run out of a lot of things before we consider something like that. I think that's really on the peripheral of things we ought to be talking about right now."
ABC News' Brian Hartman and Kate McCarthy contributed to this report.