ON THE GULF OF MEXICO -- BP embarked Tuesday on an operation that could seal the biggest offshore oil leak in U.S. history once and for all, forcing mud down the throat of its blown-out well in a tactic known variously as "bullheading" or a "static kill."

The pressure in the well dropped quickly in the first 90 minutes of the procedure, a sign that everything was going as planned, wellsite leader Bobby Bolton said aboard the Q4000, the vessel being used to pump in the mud.

He said the work could be complete by Tuesday night or today, though BP said the effort could continue through Thursday, and engineers won't know for more than a week if it choked the well for good.

The 122 crew members on the Q4000 were excited about being part of what could be the final resolution to a drama that started with the April 20 explosion on the offshore drilling rig Deepwater Horizon, Capt. Keith Schultz said.

"I'm a mariner and we lost mariners out here," said Schultz, who is on his second 28-day tour of duty since the spill started. "I'm very confident we'll be able to kill this well. It's been one magical time trying to get this thing plugged."

A 75-ton cap placed on the well in July has been keeping the oil bottled up inside over the past three weeks, but that is considered only a temporary measure.

BP and the Coast Guard want to plug up the hole more securely with a column of heavy drilling mud and cement.

The "static kill" involves slowly pumping mud down lines running from a ship to the top of the ruptured well a mile below. BP said that may be enough by itself to seal the well.

Retired Coast Guard Adm. Thad Allen, the government's point man for the spill, made it clear that to be safe, the gusher will have to be plugged from two directions.

He said the 18,000-foot relief well that BP has been drilling over the past three months will be used this month to execute a "bottom kill," in which mud and cement will be injected into the bedrock 2 1/2 miles below the sea floor.

BP won't know for certain whether the "static kill" has succeeded until engineers can use the soon-to-be-completed relief well to check their work.

Allen said the task is becoming more urgent because peak hurricane season is just around the corner.

And while the cap appears to be holding, the "static kill" would give scientists more confidence that the well won't leak again, he said.