Husband doesn't want anymore kids

My husband has always known I wanted a big family and I made sure he wanted the same thing because no kids was a deal breaker for me. We have 5 kids and I talked to him about having our 6th and he said he doesn't want anymore kids. I asked why when he knew I wanted a lot of kids and he started bringing up excuses saying how would we have the time to care for a baby along with the other kids. Our two oldest are homeschooled and they can help out. They already help out with the kids. My husband said not and that's his final answer and plans on getting a vasectomy because he thinks we barely have time for the kids we already have and he feels like anymore children and others will get even more neglected. I said plenty of people have big families. There are people with ten kids. My husband feels like we don't have enough time for the kids we already has and feels like he doesn't know anything about our oldest kid because we are always so busy and he's putting his foot down to no more kids. Would this be a deal breaker to you? I don't want to break up my family and I love my husband but I want more kids.