Copiapo, Chile (CNN) -- The 33 Chilean miners who have been trapped underground for more than three weeks spoke directly with family members for the first time Sunday, as officials worked to keep the men's spirits and health in good shape.
One person per family was given about 20 seconds each to talk through a line that was rigged to connect the miners with life above ground.
"He's good, very good. He told me to be patient and to have faith," Antenor Barrios, father of one of the trapped miners, said after talking to his son, Carlos.
Family members have mounted a constant vigil in a tent city -- dubbed Camp Hope -- outside the copper and gold mine in the Chilean desert. About a week ago, miners first sent up a written message telling rescuers they had been safely huddled in a shelter some 2,300 feet (701 meters) underground since a cave-in there on August 5.
One of the miners, Esteban Rojas, sent a letter to wife soon after the men were discovered alive, asking her to marry him in a church ceremony. The two were married in a civil ceremony and have been together for some 25 years.
"I was worried he might not mention it again, but he said we should get married in church. He'd asked me if I've already chosen the dress," said Jessica Yanez, his wife, after talking to her husband. "Of course I told him we would get married."
The couple will have to wait.
Officials estimate it could take as long as four months to rescue the miners.
"We are looking at other options, but the most important thing is that we don't have any failures and that we can rescue them at least within that period," Chilean Mining Minister Laurence Golborne told reporters.
To help the miners survive, Golborne said rescuers are sending down aluminum bed frames, towels, hot-weather clothes that wick away sweat, shampoo and shower caps. MP3 players, speakers and a mini-TV projector -- along with recordings of soccer games and other films -- are also on the way, he said.
Supplies are being passed through a bore hole, measuring about 4 inches in diameter, that rescue workers call the umbilical cord.
Chilean Health Minister Jaime Manalich told reporters on Sunday the miners were sent vaccines to protect against diseases like diphtheria and tetanus. He said the risk of infection among the men is high as they are crammed in such a small space. Some of the miners are having problems with skin fungi, Manalich added.
He said the miners currently have a video camera underground and are filming each other to show injuries they sustained during the cave-in. The images should help doctors diagnose and treat the men, though no one is thought to have serious wounds.
The miners have also been sent rubber boots and chlorine to help treat water from sources they have access to underground, Manalich said.
Chilean officials plan to start drilling a rescue shaft Monday -- a process that could take between three and four months.
But a group of engineers have said they have a "Plan B" that could reduce by half the time it would take to reach the miners.
Walter Herrera, quality control and risk manager for Chilean mining company GeoTech, has said his company was bringing a specialized device -- a Scram T-130 drill typically used for boring water holes -- to the San Jose mine.
Herrera said his plan hinges on using one of the three bore holes already made. The drill would use that hole as a pilot and widen the diameter to about 28 inches, which officials have said is wide enough for the miners to pass through.
"We think it could be quicker than the other plan. In ideal conditions, this could take around two months," Herrera said.
The Chilean mining minister has not ruled out the alternative plan, but has cautioned it might not work. He has also said it might not be put into operation.
Officials said both efforts -- to drill the rescue shaft and widen the bore hole -- could be carried out at the same time.
A four-person team from NASA is expected to arrive in Chile next week to help provide nutritional and behavioral health support to the miners. NASA has a long history in dealing with isolated environments and thinks experiences in space and underground are not too different, said Michael Duncan, the U.S. space agency's lead person on the Chile effort.
"It's an opportunity to us to bring the space-flight experience back down to the ground," he said.
Meanwhile, Pope Benedict XVI said in his weekly message from Castel Gandolfo, his summer residence, on Sunday that he was praying for the miners and their relatives.
Family members continue to keep vigil. And on a barren hillside overlooking the mine, relatives light a candle for every man fighting to stay alive underground.
"I entrust them and their families to Saint Lorenzo," the pope said in Spanish. "I'll continue to pray for them so they can remain calm as they wait for a happy resolution to the ongoing rescue efforts."
CNN's Gustavo Valdes contributed to this report.