SANTIAGO, Chile — Chilean rescuers are growing increasingly optimistic about pulling the 33 trapped miners out far sooner than originally estimated, and with drilling quickly advancing on three narrow escape chutes, they raced Tuesday to decide on a design for the capsule that will lift the men to safety.

President Sebastian Pinera has staked his presidency on being able to show the world that his government has safely rescued the miners ahead of schedule. He promised the men after they were found to be alive Aug. 22 that they would be home by Christmas – a time frame mining experts called far too conservative – and then put hundreds of rescuers to work on three simultaneous drilling operations to reach them more quickly.

The engineer in charge of the rescue effort, Andre Sougarret, said Tuesday that “it’s still premature to talk about shorter time frames. We’re sticking with the first days of November as the final date of the rescue.”

But the rescue team’s own numbers suggest faster progress. The biggest drill, labeled “Plan C,” is capable of much faster speed, and the deeper it gets, the faster engineers plan to drill.

Barring unforeseen complications, it could break through to the miners at a point nearly 2,000 feet underground in the second week of October. Sougarret has said it would then take eight days to insert an iron sleeve in the 28-inch-wide chute to prevent rock falls while miners are being pulled out.

There’s also the matter of an Oct. 15-22 European trip scheduled by Pinera, who promised the miners in a video chat Sunday that he would be there to hug them as they emerged.

While his ministers have struggled to manage expectations, Pinera could hardly contain himself when asked by reporters at the mine to commit to a date, saying with his usual broad smile that “it will be sooner than what you expect.”

In another indication of the rescue effort’s progress, Sougarret said the rescue capsule – named Phoenix for the mythical bird that burns to ashes, only to rise again and live for hundreds of years – has to be ready within 10 to 12 days after they decide on a final design this week.

With that in mind, engineers were viewing prototypes of the capsules Tuesday at ASMAR, the Chilean navy’s shipbuilding operation in Talcahuano, where three of the capsules will be built to provide backups in case anything goes wrong.