Before you create a wet mess inside the house check outside for an inspection pit - if you have one lift the lid and look inside - then you will know where the blockage is.
If you use a mop with a bag over the head it would help for the mop to be wet - you will be trying to fill the outflow from the pan to push any obstruction through the pipework.
If the inspection pit reveals a blockage it will be in the outflow pipe pointing towards the street. Try first with a flexible stick to pull the obstruction back into the pit - pushing may just make it worse. I use a 6foot length of plumbing barrier pipe - takes me 5 mins now I have the technique.
Good luck...
Peccavi, March 2011