NRE is new relationship energy. It refers to that time in a new relationship when you tend to make bad decisions because you're so caught up in the newness and the happiness and the this-is-going-to-last-foreverness and the this-is-my-soulmateness. It is, essentially, your hormones controlling you. It generally lasts from one to two years. It can literally destroy a poly relationship when someone allows NRE to influence them and neglect the relationships that are not causing the NRE. It can be addictive--you see this in the person who moves from "love of their life" to "love of their life" without settling. A friend of mine once said in reference to NRE, "One should never make decisions while high" and that is 100% true.
As for the OP, I've been in a committed poly relationship for some time now, and I'm not sure how I would handle it if any of my partners wanted more children even after all of this time together. I can't even imagine having a baby after knowing someone less than a year. Rushing into having children is, in my opinion, a big mistake. Your relationship hasn't even settled yet, and they want to add stress? And, like everyone else said, OF COURSE having children affects you. I like to help out, but that late-night changing and feeding on a child that I had no choice about, doctor's bills, clothing bills, bills bills bills and I had no say, would build resentment in even the sweetest person. You need to stop waiting for them to talk to you and have a conversation with them, together, seperate, with someone to hold your hand, whatever works. Calm but firm, assert your rights. EVERYONE has a right to be heard in the relationship, whether they agree or not.