I can give you some perspective from the other side of this situation and give you some hope.
After ~10 years of dating and being sexually compatible, my wife and I stalled a year or so into marriage. I was going to school full time and working 1-2 part time jobs and was too stressed and tired. Her parents were also living in our small house for a few months as well. My wife would bring up the lack of intimacy which I recognized as a problem, but the issue was really with the work and life stress which I really couldn't change. She would bring it up constantly and the conversation about helping me reduce stress would always devolve into me consoling her about her feelings of insecurity when I was the one who was overworked and depressed.
I finally landed a better job and got to a better mental space a couple years later and we decided to have children. I have always wanted to be a father and have worked with kids since I was in high school but I still had a lot of unreconciled resentment for the lack of support and it made intimacy difficult. We would talk about it and apologize, but I still felt angry that I was working 60 hour weeks and she was complaining about sex. She was convinced I did not want kids or was cheating on her because that's the advice she predominately received from others and the internet. We had to talk a series of long talks before I really felt like she understood how lonely and unsupported I felt during that time before I forgave her. Things started to return to normal in the bedroom after that and we're expecting twins soon and am really happy and excited.
One other thing I would mention: it infuriates me when I see posts where people say someone "isn't doing their duty" when they don't want to have sex. Sex is the emotional payday for a healthy relationship. If it isn't happening, there is a physical or emotional reason that both people need to confront together. If you take the tact that this is his problem and he needs to fix it, or he is lying to you about not wanting to have kids, he'll feel attacked and you're less likely to reach a resolution that way.