Hawkeye: Didn't USB 3.0 increase the available power? Yes, the OP should use a drive with a separate power supply, but...
USB 3.0 increased the power from 0.5 watts to 0.9 watts at a nominal 5 volts. Still pretty tight for a 3.5" HDD, at under 5 watts.
Yes they did. I wish they had boosted it just a bit more. You might be able to get away with using USB power alone, but as you stated, it will be tight. If the manufacturer provides a power adapter, then I assume it won't be able to draw enough power from the USB port.
If the OP is willing to trade off a 3.5" drive for a 2.5" drive, then he'll have more options available.