Joe, before telling this employer you would need $x to take the position, why didn't you actually THINK first about what you would need in order to take it?
At this point, you might want to tell them you discussed the job, and longer commute, with your wife, and you both felt that you would need $y to take the job. Tell them you are VERY excited about the opportunity, blah, blah, blah... but you have a young child at home and you and your wife have decided the current salary offer doesn't justify the change in time spent helping your wife raise your child, and the extra money spent on the longer commute. In other words, BE HONEST! BUT, you had better be serious about it and tell them you are ready to accept their offer NOW if you do this, no thinking about it for days or weeks or they will tell you to shove it as you will start to looking like a potential problem if you need to dwell on it any longer... indecisiveness is not what employers are looking for in a sys admin.
Let this be a lesson to others as people doing hiring do not like being jerked around and having their time wasted because people come at you with numbers that are too low, then can't make up their minds. For the few positions I've had to interview people for, it was a real PITA as the many people just want the offer letter in hand to milk their current employer. People doing the hiring know this happens, so make it clear to them that for $X you WILL ACCPET the job offer immediately once sent an offer letter.