You did not say what model Yamaha. I just did a quick search and for the model the EF2000iS- it is rated for 1600 watts (max. 2000 watts) and 13.3 amps (max. 16.7 amps) @ 120V AC.
The welding machine:
120 volts, 60 Hz, 20 amps, single phase input
Welding Output Range: 60-120 amps AC
amperage x voltage=watts
20x120=2400 watts
So, you are underpowered with a 2000 watt generator. I would think you would need, realistically, a 3500 watt unit. You really don't want to stress the generator to attempt to run it at maximum output when you use it. You may technically weld, but it won't be much.
Good luck on your search.