BP has tried and failed repeatedly to halt the flow of the oil, and the latest attempt, like others, has never been tried before a mile beneath the ocean. Experts warned it could be even riskier than the others because slicing open the 20-inch riser could unleash more oil if there was a kink in the pipe that restricted some of the flow.

"It is an engineer's nightmare," said Ed Overton, a Louisiana State University professor of environmental sciences. "They're trying to fit a 21-inch cap over a 20-inch pipe a mile away. That's just horrendously hard to do. It's not like you and I standing on the ground pushing -- they're using little robots to do this."

Engineers have put underwater robots and equipment in place this week after a bold attempt to plug the well by force-feeding it heavy mud and cement -- called a "top kill" -- was aborted over the weekend. Crews pumped thousands of gallons of the mud into the well but were unable to overcome the pressure of the oil.

The company said if the small dome is successful it could capture and siphon a majority of the gushing oil to the surface.  But the cut and cap will not halt the oil flow, just capture some of it and funnel it to vessels waiting at the surface.

BP's best chance to permanently plug the leak rests with a pair of relief wells, but those won't likely be completed until August.