Yes, chiggers can live in the carpet, etc.  Rather than using a bomb (as taddyport mentions, you have to clean everything afterwards), try using Zodiac Household Spray.  It's a flea and tick spray meant to be used on upholstery and carpets.  Check for color fastness (spray in a small corner to make sure it doesn't discolor, etc.).  Then spray everything that can't be washed - mattresses, cushions, blinds, floor.  Spray into corners.
For fleas and ticks, you would repeat the spraying in 2 weeks to kill anything that hatched after the first spraying.  I'm not sure of the life cycle of the chiggers, but a second spraying won't hurt.
I have used this stuff on chiggers and it killed them.