My father recently passed away and he had approximately $9,000 in credit card debt between two credit cards. His house was his only asset and is paid off and worth about $300K. What should I do about the credit card debt? Can the two credit card companies each force me to sell the house so they get their money?

How does title pass to you? There are at least three possibilities:
1. You are his only heir
2. He left you the house by will
3. It goes to you through some sort of trust instrument.

In case 1 & 2, you will have to go through probate, because otherwise the house doesn't automatically get transferred to your name. In that case, the credit card companies are creditors and probably will have to be paid.