How can I repair water damage to a hardwood floor under a washing machine?
If as @gbronner mentioned its just the surface layer, that's pretty easy to fix:  Scrape it clean, sand a bit, remove the dust, then apply poly.  I wouldn't necessarily recommend this in the middle of a living room floor, but in a laundry room, I at least am less concerned about the appearance of the floor.
But if those boards are soft in the middle, they definitely need to be replaced and since they are being replaced you should also take a look at the sub floor to ensure there was no permanent damage to what is underneath.  That said, If you have stopped the leakage you shouldn't have issues waiting for a contractor.  


Please clarify the scenario we are working with here, surface damage or soft/rotted wood.  If you are interested in fixing it yourself, I would suggest getting us a picture of the layout of the room (dimensions, and where the damage fits within those dimensions).  We can  suggest a best course from there.