"We do have a high level of confidence that the relief wells will permanently seal the well," McKay said.
Digging them could take months, reports CBS News correspondent Sharyl Attkisson.
"This could take us until July and early August," said Sen. Joe Lieberman, I-Conn.
"Of course we're doing everything we can to stop it before then," McKay said.
Special Section: Disaster in the Gulf
"60 Minutes": The Deepwater Horizon Disaster
White House to Create Oil Spill Commission
Oil Spill by the Numbers
There's plenty of blame to go around. The federal agency in charge of oil rig inspections - the Minerals Management Service - reportedly fell short of its own policy of holding at least one inspection a month. Monday, a top official there announced he'll retire ahead of schedule - at the end of the month.
In a "60 Minutes" exclusive, rig survivor Mike Williams said rig owner Transocean was warned of , the crew's last hope in an explosion.
"I recall asking the supervisor if this was out of the ordinary," Williams said. "And he says, 'Oh, it's no big deal,' and I thought, 'How can it not be a big deal?'"
Transocean says the blowout preventer passed tests after the incidents in question.
But the confusing sequence of events shows how unprepared everyone was:
April 20: 11 are killed after the blowout preventer fails
April 23: The Coast Guard says an oil leak may have been averted
April 24: Leaking is confirmed at an estimated at 42,000 gallons a day
April 28: A stunning new estimate: 210,000 gallons a day
May 9: BP's attempt to use a containment dome fails
May 12: Some now estimate leakage at more than 2 million gallons a day
May 14: BP hopes a tube will collect most of the oil
May 17: The tube is siphoning -- but only about a fifth of the oil
"It feels like you're making it up as you go along," said Sen. Susan Collins, R-Maine.
BP and the federal government have had to admit that's more or less the case. That's prompting and across-the-board rethinking of contingency plans and emergency response for offshore drilling.