"Trabajo tanto como tú."
'tanto' is for expressing degree of quantity, not similarity of manner. I work as much peeling potatoes as you do scrubbing floors, but our work is not similar.
Your response makes sense. However if one mouses over it it only lists "so much" not "as much"
Time to go back to some other methods of study to build my vocabulary and comprehension of the actual ways words are used in the Spanish language. Thank you rspreng for another helpful explanation.
The Spanish version seems to indicate to me that there is a LOT of work going on as well as the equality of work being done. The English translation only captures the equality. You and I may be doing very little work but it is equal. Perhaps this would be better translated "I work a lot, just like you" or something like that.