“What we’re focusing on now is creating conditions that will allow us to enter the chamber behind the cutter head and see what the situation is,” Chris Dixon, the project manager at Seattle Tunnel Partners, the construction contractor, said in an interview this week. Mr. Dixon said he felt pretty confident that the blockage will turn out to be nothing more or less romantic than a giant boulder, perhaps left over from the Ice Age glaciers that scoured and crushed this corner of the continent 17,000 years ago.

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But the unknown is a tantalizing subject. Some residents said they believe, or want to believe, that a piece of old Seattle, buried in the pell-mell rush of city-building in the 1800s, when a mucky waterfront wetland was filled in to make room for commerce, could be Bertha’s big trouble. That theory is bolstered by the fact that the blocked tunnel section is also in the shallowest portion of the route, with the top of the machine only around 45 feet below street grade.

“I’m going to believe it’s a piece of Seattle history until proven otherwise,” said Ann Ferguson, the curator of the Seattle Collection at the Seattle Public Library, who said she held out hope for something of 1890s Klondike Gold Rush vintage, when Seattle became the crazed and booming gateway city to the gold fields of Alaska and Canada.

At the downtown storefront museum for the tunnel project, called Milepost 31, visitors are cracking Jimmy Hoffa jokes or spouting theories about buried train engines. Gabe Martin, a sales clerk at a curio shop near the dig site, said he was intrigued by the Prohibition era, when Seattle rode a tide of illegal alcohol smuggled from Canada, and people had reason to bury things, not wanting them found. “Bootlegger stuff,” he said.

Mr. Dixon said that efforts to drain water and reduce pressure at the drill head, with a series of bore holes pushed down in recent days, could allow workers to get safe access to the blocked site as early as Friday. But working at atmospheric pressures similar to what a diver would experience, the team could stay down only for short periods, he said, and each visitor would then need time in a decompression chamber.