SAN JOSE MINE, Chile — Chile’s trapped miners cheered and embraced each other Saturday as a drill punched into their underground chamber, opening a way out with a spray of rock and dust from the collapsed mine where they have been stuck for an agonizing 66 days.

More than 2,000 feet above them, rescue workers also celebrated, dancing and spraying champagne with such excitement that hardhats tumbled off their heads.

Family members chanted and waved flags, then everyone braced for the next challenge: Rescuers must decide whether it’s riskier to pull the 33 miners directly up through unreinforced rock, or to insert tons of steel pipe into the curved shaft in an attempt to protect them. The answer will determine whether their pullout begins Tuesday, or up to a week later.

“We still haven’t rescued anybody,” Mining Minister Laurence Golborne said. “This rescue won’t be over until the last person below leaves this mine.”

Still, completion of the escape shaft was a major cause for celebration. Miners who assisted the drilling effort by clearing fallen rock and videotaping the machine from below were ecstatic when it finally penetrated the chamber.

“On the video, they all started shouting and hugging and celebrating,” said James Stefanic, operations manager for the U.S.-Chilean drilling company Geotec.

In the makeshift hillside community known as “Camp Hope,” where family members have held an anxious vigil since the mine’s partial collapse Aug. 5, the breakthrough of the escape shaft was a tremendous relief.

“We feel an enormous happiness,” said Darwin Contreras, whose brother Pedro, a 26-year-old heavy machine operator, is stuck down below. “Now we just have to wait for them to get out, just a little bit longer now.”

Contractor Jeff Hart of Denver operated the drill, pounding through solid rock and the detritus of the collapsed mine, which corkscrews deep below a hill in Chile’s Atacama desert.

“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.”

While the “Plan A” and “Plan C” drills stalled after repeatedly veering off course, the “Plan B” T130 drill reached the miners at a point 2,041 feet below the surface at 8:05 a.m. local time, after 33 days of drilling.

The milestone thrilled Chileans, who have come to see the rescue drama as a test of the nation’s character and pride.

“When we Chileans set aside our legitimate differences and unify in a grand and noble cause, we are capable of great things,” President Sebastian Pinera said in a triumphant speech at the La Moneda palace in Santiago.

But the next decision is terribly difficult: Rescuers must determine whether it’s riskier to pull the miners through unreinforced rock, or to insert tons of steel pipe into the curved shaft to protect them on their way up.

While Pinera has promised “to do everything humanly possible” to keep the miners safe, attempting that now might make things worse.

The decision will be purely technical, Golborne said, made by a team of eight geologists and mining engineers based on a video examination Saturday of the shaft’s walls.

But the political consequences are inescapable. While engineers have said there is only a remote chance of something going wrong if the shaft remains unreinforced, Chile’s success story would evaporate if a miner gets fatally stuck for reasons that might have been avoided.

Some of the miners’ families have lobbied to line the shaft with truckloads of heavy steel pipe that have been brought in, just in case. But the benefit may not prove to be worth the risk, Golborne said. While half-inch-thick steel would prevent stones from falling and potentially jamming the capsule, the piping wouldn’t save a miner if the unstable mine suffers another major collapse, and the process of installing it could itself provoke a disastrous setback.

“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 easy decision to make.”

If the shaft proves to be strong and uniform enough to let the capsule pass without significant obstacles, rescuers plan to start the rescue Tuesday.

First, a Chilean navy paramedic and a mine-rescue expert will be lowered down through the shaft to prepare the men. Then they’ll be strapped one by one into the capsule and pulled out by a huge winch in a spectacle carried on live television.

“Whether it’s Tuesday, Wed-nesday or Thursday isn’t important. The important thing is to rescue them alive and safe,” Pinera said.

The miners will be initially examined at a field hospital where they’ll be allowed to briefly reunite with up to three close relatives. Then they’ll be flown by helicopter in small groups to the hospital in Copiapo, capital city of the region, where 33 fresh beds await. Only after their physical and mental health is thoroughly examined will they be allowed to go home.

“I’m very excited, very happy,” Guadalupe Alfaro, mother of 26-year-old trapped miner Carlos Bugueno, said as she waved a Chilean flag outside her tent. “I’ve wanted so long for this moment, I woke up to live this moment. My son will return soon.”