Our fridge (not a Whirlpool, though) did something similar - it turned out the water was perfectly normal, but it was supposed to drain away through a drain hole which was blocked. Once this was sorted, it's been fine.
As mentioned above the channel at the back of the fridge for clearing the water becomes blocked and the water then finds a new route which is normally down under the vegetable containers and possibly out onto the floor. I've seen this happen in the past where small pieces of food fall down at the back of the fridge and block the outlet. IMHO if you have hard water this over time can block it also. I've cleared some of them with the help of a cotton bud.
Its just a question of taking out the vegetable holders and with the help of either a cotton bud or possibly J cloth you can usually clear out the blockage.
We've had the same issue, and yes it was a blockage.
My recommendation for clearing out anything that as build up is to use a drinkingstraw (the ones with the bend in them are the best). YOu can find that whatever is blocking can be brought up in the straw...