SAN JOSE MINE, Chile - A drilling rig punched through to the underground purgatory where 33 miners have been trapped for 66 agonizing days under the Chilean desert, raising cheers, tears and hopes on Saturday.

Champagne sprayed and hard hats tumbled off heads as rescue workers pressed close to the drill, hugging each other and shouting for joy. Down in "Camp Hope," where the miners' relatives waited, people waved flags and cried as one man energetically rang a brass bell even before the siren sounded confirming the escape shaft had reached the miners.

Chile's mining minister said that the 33 miners trapped for more than two months will probably be pulled out starting Wednesday.

That's because the rescue team has decided to reinforce less than 315 feet of the rescue shaft in steel pipe.

The rest of the escape shaft is exposed rock, and the rescue team has decided it's strong enough to provide for a smooth ride for the miners' escape capsule.

Mining Minister Laurence Golborne set the date after the shaft was inspected with a video camera Saturday following the completion of the hole earlier in the day - a success that set off celebrations by the miners underground and by their families and rescue workers on the surface.

"We feel an enormous happiness, now that i'm going to have my brother," said Darwin Contreras, whose brother Pedro, a 26-year-old heavy machine operator, is stuck down below. "When the siren rang out, it was overwhelming. Now we just have to wait for them to get out, just a little bit longer now."

Jeff Hart of Denver, Colo., operated the drill, and said the entire rescue crew erupted with cheers when the T130 broke through.

"There is nothing more important than saving, possibly saving 33 lives. There's no more important job than that," Hart said. "We've done our part, now it's up to them to get the rest of the way out."

The milestone thrilled Chileans, who have come to see the rescue drama as a test of the nation's character and pride, and eased some anxiety among the miners' families.

But now comes a difficult judgment call: The rescue team must decide whether it's more risky to pull the miners through unreinforced rock, or to insert tons of heavy steel pipe into the curved shaft to protect the miners on their way up.

"This is an important achievement," Mining Minister Laurence Golborne said, "but we still haven't rescued anybody. This rescue won't be over until the last person below leaves this mine."

President Sebastian Pinera promised "to do everything humanly possible" to keep the miners safe, and as the drill was nearing the breakthrough, he said he had kept his promise.

Those in charge of the rescue say the decision on how to proceed next will be a purely technical one.

While engineers have said there is only a remote chance of something going wrong, everyone involved knows how terrible it would be - politically as well as for the families - if a miner gets stuck partway up for reasons that might have been avoided.

Steel pipe would prevent stones from falling and potentially jamming the capsule, but it wouldn't save a miner if the unstable mine suffers another major collapse, and might itself provoke a disastrous setback, Golborne said.

"You would have to put though a 600-meter hole a lot of pipes that weigh more than 150 tons," he warned. "And this structure can be set in a position that also could block the movement of the Phoenix (escape capsule). It's not an decision easy to make."

If Saturday's close video examination persuades engineers that the shaft is smooth, strong and uniform enough to let the capsule pass without significant obstacles, then rescuers plan to start pulling the men out one by one as early as Tuesday, in a made-for-TV spectacle that has captivated the world.

The miners will be initially examined at a field hospital where they can briefly reunited with up to three close relatives. Then, they'll be flown by helicopter in small groups to the regional hospital in Copiapo, where 33 fresh beds await and they will be observed for at least 48 hours. Only after their physical and mental health is thoroughly examined will they be allowed to go home.

"I'm very excited, very happy," said Guadalupe Alfaro, waving a flag outside her tent. Her son Carlos Bugueno, 26, is stuck down below. "I'm very excited, very content. I've wanted so long for this moment, I woke up to live this moment. My son will return soon."

"Our nervousness is gone now," said Juan Sanchez, whose son Jimmy is stuck in the mine. "Only now can we begin to smile."