Copiapo , Chile ( CNN ) -- The first of the 33 miners trapped underground for more than two months could be hoisted to safety as early as Wednesday , Chilean Mining Minister Laurence Golborne said Saturday . He spoke hours after anxious family members and exhausted rescue workers reveled in joyful relief after a drill pierced the roof of an underground mine in Chile where the men have been trapped since August 5 . Sixty-five days after the mine 's collapse , officials announced the drill had reached the miners as sirens blasted through the site to signal the achievement . Family members ran downhill , cheering and carrying Chilean flags . What began as a `` possible tragedy , with the help of God , is ending as a true blessing , '' said Chilean President Sebastian Pinera . `` The miners , their families , the rescue workers , the government and all the Chileans have shown unity , strength , of faith , of hope , that is recognized and admired by the whole world , '' the president said . `` This shows that when Chileans unite for great causes , regardless how grand or ambitious they may seem , we are always able to reach our goals and conquer the highest peaks . '' Still , despite the day 's success , rescue workers continue to face tough decisions and hard work to get the men out of the mine . `` We have not yet rescued anyone and there is much ground to cover , '' cautioned the mining minister , who also told reporters that the families of the miners `` are aware of the process still expected . '' Later in the day , Golborne said he believes workers could begin to hoist the miners up by Wednesday . The rescue operation is likely to take around two days , he said , which would mean all 33 men could be pulled to safety by Friday . Also Saturday , the miners successfully set off explosives in the mine to widen the rescue shaft through which they will be brought , Golborne said . Mine engineers decided to encase just the top part of the shaft with steel tubing to prevent rockfalls and further collapses during the extraction process . Previously , they had thought they might need to encase the whole thing -- a process which would have delayed the rescue . Raul Lyon , vice president of GeoTech , the company operating the Plan B rescue drill at the scene , told CNN , `` I ca n't wait to see the first one to come out . '' Lyon said the ordeal has been arduous and emotional for the workers , but `` we had patience '' and solved problems methodically as they came up . `` It was very exciting and also comforting that we were able to reach the tunnel after exactly 33 days of drilling , '' said Lyon , who noted that the miners are `` happy '' and `` in good shape . '' Rescue crews have been drilling three separate wider holes to send down the rescue capsule and hoist the men to the surface . Those rescue attempts have been labeled Plans A , B and C. Brandon Fisher , owner of the Pennsylvania company that provided and oversaw the use of drilling bits for the Plan B team , felt a `` huge sense of relief and joy '' and noted that the success was n't `` in the bag until we were through . '' `` This project was unbelievably challenging , '' said Fisher , whose company , Center Rock Inc. , aided in the rescue of nine miners who were trapped for more than four days after the 2002 collapse of the Quecreek Mine , also in Pennsylvania . After the 2,300-foot hole in Chile is secure , materials and equipment will be brought in so that the rescue capsule -- dubbed the Phoenix -- can be lowered into the mine . Then , authorities will lower a doctor and a rescuer into the chamber , Health Minister Jaime Manalich said . Medical and rescue personnel will be in place to start extracting and treating the miners . Once the men have been extracted , they will undergo about two hours of health checks at a field hospital set up at the mine . They will then be flown by helicopter to a hospital in the town of Copiapo -- approximately a 15-minute flight . `` You think we were happy , you should have seen those guys , '' said Gregory Hall , one of the rescue drill operators , after Saturday 's breakthrough . `` They were just going crazy . I mean , imagine , that 's a big step towards coming home . So they were just going crazy . It was wonderful . '' Miners who are healthy enough will be allowed to visit briefly with family members in a reunion area before being taken to the hospital , Manalich said . Health officials have increased the miners ' physical activity in recent days to gauge how they can handle the stress of being removed , the health minister added . The overall response has been good , he said , though some miners have exhibited anxiety or have had minor cardiac issues . The miners have been in contact with the outside world through a small bore hole that sends them food , water , supplies and other necessities . Pinera said September 19 , during his last visit to the site , that he planned to personally hug each of the miners as they were pulled from the rescue shaft . He is due to depart on a government tour to Europe in mid-October . First lady Cecilia Morel Montes told reporters Friday night that her husband was in the south . `` He has a lot of obligations , '' she said . `` Undoubtedly , he would like to be here permanently . But he also has to be permanently in a lot of other places and it 's necessary to continue governing . '' She said the crisis faced by the miners has brought Chileans together . `` They have become very familiar to every Chilean , '' she said . `` All Chileans are equally expectant , equally nervous ; there 's a lot of empathy toward the families . '' She added that the men 's liberation will occur `` as soon as possible , '' but only after every precaution is taken to ensure their safety .
NEW : The first of the men could be pulled above ground as early as Wednesday , official says . A second man is still missing and a third was found dead in an area about 20 miles from where he had been found. Rescue workers still face a multitude of challenges . The men have been trapped since August 5 .