Eventually, I want kids. I strongly feel that producing spawn is something we "should do", call it religious or whatever you want. Therefore, any woman who fervently does *not* want children will not be one I end up with. That means that any "liaison" we would ever have, would be nothing more than a casual fling. Casual flings are great, but they're not relationships. so yes, it would affect my desire greatly.
Small anecdote that ties in very well. Talking with friends after class, the topic of kids came up. One gorgeous blonde was adamant that she didn't want kids ever. She instantly got relegated into my "friend-zone". Would I take her on a weekend trip to a log cabin? Sure, sounds like a steamy good time. Would I make any kind of effort to start a relationship with her? No, what'd be the point? Eventually, that relationship would collapse if she was really adamant about remaining childless. It surprised me how much less attractive she appeared to me after uttering that sentence. Still as pretty, sure, but a lot less attractive.
Also, I feel a lot of dudes are picking the "no, it wouldn't affect me." option without thinking. If you're still young and think that someone who prefers to remain childless is a better choice for a relationship than someone who would eventually want kids then your answer needs to be "yes, it would affect me." It'd affect you in a positive way.