New York is currently building a 3-kilometer tunnel between Brooklyn and Staten Island, using the same EPB method that Madrid uses to build subway tunnels. The cost of the single-bore tunnel is $250 million, and the project will be completed by 2014.
Of course, this is a water tunnel rather than a train tunnel. The diameter of the tunnel is somewhat smaller than that of a single-track train tunnel. Double-track tunnels, even ones built to high-speed rail standards, are substantially wider, but the amount of concrete lining required is proportional to radius rather than to cross-sectional area. For example, the double-track Seikan Tunnel is 9.7 meters wide, little more than single-track HSR tunnels in Europe, as Japanese construction tries to minimize tunnel clearances to cut costs and instead equip Shinkansen trains with elaborate aerodynamic noses. While 9.7 is more than 2.5 times the diameter of the water tunnel in question, 250 million times 2.5 is still far below the construction cost of any recent tunneling project in New York.
The expensive part of tunneling, then, is not the actual tunnel. It’s everything else, especially the station caverns. Both ARC and East Side Access included multilevel deep caverns in Manhattan with full-length mezzanines; of course they’d be more expensive.
For what it’s worth, an 8-kilometer long, 9.7-meter wide tunnel from Staten Island to Manhattan would cost $1.75 billion at the same per-km, per-meter cost of this water tunnel. Of course stations at St. George and especially Lower Manhattan would add much more, forcing a lot of difficult choices about location, but the basic infrastructure is not all that expensive.