Yup, diesel will slowly eat most regular gas cans. Not in the course of an hour, or anything, but you do need a different can. Diesel cans don't cost that much more, though.
How much (reusable) mineral spirits are you cranking through that $7 a gallon is a problem? If you're that worried about price, I'd stay with the spirits anyway -- comes with its own can.
Vegastriker is right about the evaporation, as well. Stuff soaked in diesel, particularly a chain, will take a while to dry.