Okay, I found someone that's got a more sensitive DC ammeter. I measured my TL082-based straight-cmoy amp, and it draws 6.4 mA at idle with no headphones plugged in, 6.5 mA when my HD570s are in, and ranges from 8-12 mA while playing music at a good rockin' volume.
I just got some OPA2132s in, and popped one in to test. The amp draw actually went _up_, which I found odd. At idle, it's more like 6.8 mA, and while playing it's 11-15 mA. It's too bad that these 2132s are less efficient, since most people run them with only one battery -- you halve your mAh, then get less play time out of each battery to boot! I may be wrong on that, though -- since they'll tolerate low voltages better than the TL082, they may actually run longer, despite their higher current draw. I'll have to test that....
Getting back to the TL082 version, the 6.4 mA at-idle draw means that if you left the amp on, it would last 8 days before completely killing the batteries, and will stop making sound well before that. It doesn't really say on the data sheets how much voltage it needs, but it hints that it will barely function at +/- 4.5 VDC. I did test with only one 9V battery, but I seem to recall being dissatisfied with its performance.