Watts works for RMS voltage, AC, DC square wave or triangular wave. Where the calculated power fails to match motor 'power' is in a couple of areas:
1) Surge power on start. VFDs can be set to ramp up and minimize the surge that a directly connected motor will give.
2) Motor efficiency - most motors are below 100%, most in the range of 80% in the size that we're talking about.
So a 2HP 120V single phase VFD rated at 2HP out at 240V 3 phase could run a 2HP motor while drawing right at the 15A limit when the motor is under max stress, most of the time draw would be a lot less. It's right at the top end of what you can do with the 15A wall socket, and I'd really feel more comfortable if you were using a utility outlet (20A) rather than a convenience outlet (15A) just for the headroom. But you could run a 2HP mill off the 15A 120V outlet.
If I were doing this I'd just pull a big-ass extension cord from the electric dryer outlet, or put a non-code pigtail from the electric over or range breaker to an additional outlet - something I could pull from the box when I had to.