I have been through this as the rejecter. I said most of the things your fiance said, and my partner said most of the things youre saying. During this time, I was on the pill (completely cut my libido), very stressed about work, exhausted every damn night. I had been through the most ill years of my life. I had my weekends constantly overbooked and had nothing to help me relax. There was no time to just "be" with my partner, so I certainly didn't want to be intimate with him! For me, I can only be intimate when we are also being randomly cuddly during the day/week.
Couples counseling is the best thing you could possibly do. To get through it, we did the following:
Went to separate psychologists. We had started this as things went downhill, but we also went to a couple of sessions with the other person and their psychologist.
I got off the pill. He was very resistant to it, both for possibility of getting pregnant and my periods becoming more painful (the reason I'd gone on it), but I'd started other solutions for periods and we're very good with condoms now!
We started regular no-pressure touching, eg hugs, massages of head/back/feet, just holding each other.
We also improved the crap out of our lives. Cut back weekends to one, maybe two outings. I switched projects and offices at work. He finished his degree and has a temporary job. We spent a lot of time talking about everything and going on walks. It took a lot of effort from him when he felt he was just going to get rejected for everything (he kept doing sweet romantic things) and from me to start doing those things for him.
This is a very important thing to read. There can be many things causing this. I too have been in the situation as the rejector, and stress, lack of sleep, many things can cause it.
We went a year after our first kid with none.
There were times that I didn't want him to touch me because I didn't want sex. I wanted a cuddle only, and I was afraid he'd push for sex.
We've had pretty long dry spells after #2 also. Not getting much sleep at night, wakeups from the little one, stress at work, no time to relax. Plus I don't want another baby and it took him 2.5 years to go through with the snip. Sometimes, I'm not in the mood!! And, I was tired of being the only birth control.
Frankly, I wouldn't START my marriage like this (ours didn't start this way either). It's important to find a middle ground. There will be ebbs and flows, but you have to make sure it's not 100% ebbs. And that means for the person doing the rejecting, sometimes you just have to go with it. I married a husband, not a roommate. (Plus I find the more you get, the easier it is to get in the mood). I find that I have to make time for snuggles, and sometimes just make time for a quickie.