My fiancé has 2 children with his ex (never married). When we get married will I be responsible for paying child support if for some reason he cannot (lets say he is unemployed). Does the amount of child support get based on his income or our combined income?

It is based on his income ( or based on a state required amount) some states have a minimun regardless of income.

But his being unemployed is not an excuse not to pay child support, and there will be due. You can request lower child support if he is not working but if he is out of work and does not get a lower amount, and can not pay the support or even the lower support, he will just keep getting behind and behind.

If he gets too behind they can find him in contempt

If you file your taxes jointly or with his name on them, they may be able to intercept your tax returns.

The child support is his responsibility, not yours. It is based on his income alone. You will never be responsible for supporting his kids. However, if at some point he'd be "unable" to pay (due to unemployment, disability, etc.) it's unlikely that he'll just be let off the hook completely. He may get the amount reduced and/or have to pay arrearages later but he'll have to pay ultimately, one way or another.