Petsmart carries a large critter keeper that you could use for a short term hospital tank. Get the biggest size they have. Should run you less then 15$.

It could dissolve fairly quickly. If it sits for a little while, soaking up water, then your frog disturbs the water by hopping in it could break it up pretty quickly. The other day I noticed a log in the water, tried to scoop it out and it just became mush and ended up having to dump the whole bowl (I'd just filled it XD). It had only been an hour or two. If this is it the dish would literally be caked in what would look like substraight.

Putting him in the critter keeper for a few days should clear up if he is or is not pooping in the water. Dont put a water dish in the keeper (unless your doing the warm baths), just keep it well misted so that the paper towels are very very damp. If you dont see anything in a day or two you need to try a vet. Most vets have payment plans that should be able to help. ^^