dr phill did a show on this not too long ago. i do believe he said it was not an issue, but id talk to a genetic counselor before going into this
my understanding is that yes, it would affect your children. the genetic family tree needs fresh dna in order to avoid some of the nasty deformities and developmental retardation issues that can occur. that's the main reason the whole making it illegal to marry a first cousin law came about. your family tree needs to branch out, not go straight up. i would speak to a genetic counselor on this. it could be very risky
From my understanding there are quite a few states where it is indeed legal. My grandfather from my dad's side married his cousin after his wife died, but then again they were past childbearing years. At first it upset the family, but then they realized that they really did care about each other and wanted to be together. They were actaully pretty sweet together. As far as whether it could affect offspring, that might be something you might want to check with your doctor. I'm really not sure about that. Marrying within the family is not unheard of. They were doing it all the way back in Biblical times. I'm just honestly not sure if it would affect any future children. Don't think about it, though, until you check with your doctor. That's my advice. Hope everything works out for you.
If you are in the US--I beleive that this would be illegal--this would be your first cousin and people would say this is inbreeding and way to close to the same DNA--so you could have problems later on with your offspring--but you may not--it is hard to say for you never know what DNA will combine.