First off, you will need to clean the feces off your rabbits bottom if you haven't already. If left on there it can irritate the skin and can even dry and plug up the opening. You will probably have to do a butt bath(NOT a full bath) if it is as bad as it sounds. You do need to try and minimize the stress of bathing though, so your rabbit doesn't get overly stressed from it, and you also need to make sure your rabbit stays warm until thoroughly dry.
http://www.disabledrabbits.com/baths--cleaning.html
Next, you really need to take your rabbit to a good rabbit vet asap! For your rabbit to be having that much mushy poop, it could indicate a serious problem such as a parasite or bacteria, in which case you will need the appropriate medication.
Mushy poop can also be caused by a rabbits diet. In a few cases, sudden introduction of a new food or a certain veggie or food, can cause this to happen, but more often it is caused by too many sugars and carbohydrates in the diet and not enough fiber. Rabbits need a lot of indigestible fiber to keep their digestive tracts functioning well. They get this from the addition of grass hay in their diet. Not enough fiber and too many sugars and carbohydrates from pellets or treats, can cause the overgrowth of harmful bacteria in the rabbits cecum, which leads to dysfunction and mushy poop, which can then lead to other health problems which can be fatal if not treated swiftly and correctly.
The best way to get the mushy poop to clear up is to feed only unlimited grass hay(timothy, orchard, brome, meadow, etc), for several days to weeks, until there is no soft poop for several days, then gradually adding pellets/veggies back into the diet, one at a time and slowly, starting off with small amounts and gradually increasing. You do need to make sure that your bunny is eating the grass hay really well if it is not used to eating hay, as some rabbits that aren't used to hay won't eat it even if they are starving. And you want to feed as much hay as your rabbit wants to eat and continue doing that even when adding back in pellets or other food. You won't know whether or not your rabbit will be able to tolerate pellets anymore or the amount you will be able to feed, until you start adding them back into the diet(slowly), but you won't be able to feed the same amount of pellets as before or the mushy poop is sure to come back. At the first sign of mushy poop, you should decrease the pellet amounts til your rabbit no longer has mushy poop. This rabbit should never have any sugary starchy treats either. So if this is diet related, a change of diet can often fix the problem, but if it has advanced too far and there is too much of an overgrowth of bacteria, or there is a parasite causing this, then only medications from the vet will help correct this.
http://rabbit.org/vet-listings/
http://www.sawneeanimalclinic.com/downloads/chronic_intermittent_diarrhea_in_rabbits.pdf
http://www.therabbithouse.com/diet/
