Holy crap - I did it.  Despite feeling like crap (although vast quantities of lemon tea have helped,) and expecting to put in a sub-par performance, I actually hit my treadmill goal.  I did two miles in thirty minutes.  Barely - the counters clicked over together, but not only does that count, it counts cleanly.  And I hit the first mile clean in the first fifteen minutes - I had something like ten or fifteen seconds to spare.

2.00 miles in 30 minutes
2.21 miles in 35 minutes total, with cool-down

This week instead of obsessing about how far I was getting in what sort of time, I rather aggressively ignored both the time and mileage counters, and just tried to stay as close on to 4mph as I could - except when the music really rather demanded a quicker pace.

Now let's see if I can do it twice...