New Orleans ? The best hope for stopping the flow of oil from the blown-out well at the bottom of the Gulf of Mexico has been compared to hitting a target the size of a dinner plate with a drill more than two miles into the earth, and is anything but a sure bet on the first attempt.

Bid after bid has failed to stanch what has already become the nation’s worst-ever spill, and BP PLC is readying another patchwork attempt as early as Wednesday, this one a cut-and-cap process to put a lid on the leaking wellhead so oil can be siphoned to the surface.

But the best-case scenario of sealing the leak is two relief wells being drilled diagonally into the gushing well — tricky business that won’t be ready until August.

“The probability of them hitting it on the very first shot is virtually nil,” said David Rensink, incoming president of the American Association of Petroleum Geologists, who spent most of his 39 years in the oil industry in offshore exploration. “If they get it on the first three or four shots they’d be very lucky.”

The relief well drilling and temporary fixes were being watched closely by President Barack Obama, who planned to meet for the first time today with the co-chairmen of an independent commission investigating the spill.

A senior administration official said the meeting will take place at the White House. The official spoke on condition of anonymity because the meeting had not been formally announced. For the relief well to succeed, the bore hole must precisely intersect the damaged well. If it misses, BP will have to back up its drill, plug the hole it just created, and try again.

The trial-and-error process could take weeks, but it will eventually work, scientists and BP said. Engineers will then pump mud and cement through pipes to ultimately seal the well.

As the drilling reaches deeper into the earth, the process is slowed by building pressure and the increasing distance that well casings must travel before they can be set in place.

Still, the three months it could take to finish the relief wells — the first started May 2 — is quicker than a typical deep well, which can take four months or longer, said Tad Patzek, chair of the Petroleum and Geosystems Engineering Department at the University of Texas-Austin. BP already has a good picture of the different layers of sand and rock its drill bits will meet because of the work it did on the blown-out well.