can a man fight child support?

So me and my child's father I am 6 months pregnant by got into an argument over me having my child I have by someone else there. It was such a stupid argument and to summarize things he called the police and said I had been staying at his house and driving his car while he was gone and he told me not to (showed proof that he lied)(he's in vegas on vacation). Anyway, I was told by the police to not go back (I do not have a vehicle so I was stranded for over an hour) meanwhile I'm 6 months pregnant by him, outside in 90+ degree weather with my 11 month old son... he keeps calling asking me to say that I will not put him on hold support and if I do he claims he has a really good lawyer to ha doe itt... can he ligitametely fight child support and I not get anything at all?