Yes. In fact, you can kill fleas with baking soda alone and it's gentler on carpet and rugs.
First treat all pets with a flea bath. Flea shampoos are available at pet stores and most grocery and drug stores. If treating a cat, make sure you use a flea shampoo made for cats. Flea shampoos that are made for dogs can harm a cat.
After treating your pets:
Sprinkle baking soda on your carpet and furniture. You will want to use a generous amount.
Once the carpet and furniture is covered you will want to rub the baking soda into both using a broom. You want to make sure the baking soda gets down to the base of the carpet where fleas are laying their eggs.
Leave the baking soda on the carpet and furniture for 48 hours and then vacuum thoroughly.
Once you are done vacuuming you will want to remove the vacuum bag and put it in a freezer bag. You will want to put the bag in the freezer for at least twenty four hours before throwing it in the garbage. This will ensure that the eggs can not hatch.
Repeat this entire process for a week to ensure the fleas are completely gone. It may seem time consuming, but it is much better then having to fumigate your entire house.
I would use baking soda, as opposed to Diatomaceous Earth (DE). Yes, DE works, but DE also cut lungs in both people and pets, so it's dangerous. Baking soda is gentle on people but will kill the fleas.
I would also use baking soda as opposed to Borax. Borax is a poison that is harmful to people and pets. Plus, it has been banned in many countries.