MrsMc = I have not read all the posts. Just wanted to say that our 4th child is now 4. I did read the post where you have given the reasons your husband gives for not wanting this 4th child.
He is so right. We have had rubbish holidays in comparison to what we could have had if we only had 2 or 3 children. My children even miss out on things like ice creams in the park (not always but sometimes) because x everthing by 4 is very expensive. We rarely eat out, I know my children hear their peers talking about being out at cafe's, restaurants etc. with their parents.
Time - I wish I had so much more time to give to each of my children. They need it and I don't have it. I feel so guilty about this at times. Sometimes we joke about which child we would give back!
I do at times feel I am drowning in it all. A couple of months back 2 of my children had serious health issue's. I am now looking into some form of counselling to help me cope with these health issues.
I miscarried my fourth pregnancy. Found out I was pregnant and Dh asked me to have an abortion. Our youngest was 9 months and she had been such a hard baby. Never slept for more than 3 hours at a time. Cried so much more than the previous 2. Basically she just hated being a baby! Dh said he knew he couldn't do it again. He couldn't go through the sleepless nights etc again. I was absolutely devastated that he felt this way. I didn't sleep for 2 nights thinking I had to abort for him and my other 3 kids but knowing about the guilt I would feel. A couple of days later he told me he understood I couldn't abort and it was my body so he wouldn't ask me again. Anyhow, I miscarried a week later. It was all just awful. We had a few discussions after the miscarriage. Not heated or anything just kind of frank conversations. He said he would have been happy if I had wanted to abort our 3rd pregnancy. He was talking about our 10 month old baby up the stairs sleeping. I found that so hard to hear. I was so upset, for our daughter, for us, for my family. He said he didn't ask me then because he knew I woudln't. He did get the snip when our 3rd child arrived (she was about 3 days old!). I fell pregnant for the 4 time 9 months after the snip. That was the pregnancy that I miscarried.
He said he phoned the vasectomy clininc after my miscarriage and spoke to the doctor who had preformed his vasectomy who told him it was a miracle I had been pregnant. The doctor apparently told him I could't have been pregnant by him! Told him to send in another sample,which he did and phoned him back with results confirming above again!
Needless to say 8 months or so after the miscarriage I was pregnant again. Dh didn't mention abortion this time. Obviously I knew he would have been delighted if I had got an abortion.
We do struggle with money and time. We don't have any family support and it is incredibly hard at times. We are managing to muddle through, our 4th child has ended up having health issues so it has been really, really hard at times. Our children are 12, 9, 7 and 5.
We do manage 4 or 5 nights out a year as a couple without the children which is lovely. We really treasure those nights 
It was so hard when dd3 was a baby and then when ds1 was a baby (baby number 4). We were lucky that ds1 was a very, very easy baby. He is Mr Laid Back. He just slotted right in.
i think this helped Dh. Not that he hasn't or didn't love the first 3 children, he did and was and is a fantastic Dad to them. Having the fourth child come along as such an easy baby. one who would sleep sometimes, one who was happy watching the world go bye. Really helped us bond with him. Or maybe it was just benign neglect that made us feel he was an easy baby 
.
Don't know what I am trying to say, just that it may not be as bad as your husband fears.