We had this problem a couple of years ago. I remember lying on the floor, reading the newspaper and seeing about fifteen of the little buggers hopping about on the paper. It got quite serious when one of our children developed an allergy to the bites.
There's nothing else for it; call a pest controller to come and spray your house (the larvae - like tiny white worms - live in the carpet until a suitable host comes along) and get some 'Frontline' * from your Vet (for the cat!)
The infestation should clear up in a few days.
*Or whatever they call it in America; small 'pipettes' of stuff you apply to the back of the cat's neck once a month.
Man, proud man, drest in a little brief authority, most ignorant of what he’s most assured,
his glassy essence, like an angry ape, plays such fantastic tricks before high heaven,
as makes the angels weep.
William Shakespeare (anticipating George W Bush?)