I think that if he wants a vasectomy then that makes a very clear statement, and IMO you have to admire him for that at least. Lots of men would be happy to say they don't want any more children but wouldn't be prepared to be the ones to go through with being the ones to facilitate that, iyswim.
You say you wish you'd talked about it before you'd got married, but tbh there are no guarantees with children, and you can't possibly know for certain how it will be until you've actually had them, so you could agree pre marriage on four children and end up only wanting one, or vice versa, it's simply not something you can agree on before the event.
In terms of this being a dealbreaker, I'm afraid to say that this isn't just about you any more, you have other children to consider as well. And there are no guarantees. What you have to ask yourself is whether being a single parent of two children is preferable to being married with two children, because if you split there's no knowing that A, you would meet someone else, and B, that you'd even be able to conceive again. Imagine splitting up your family only to discover that you were unable to conceive another child, or that your knight in shining armour had a low sperm count and you couldn't have a child with him either.
If you were posting that you were the one not wanting any more your dh would be slated on here. There would absolutely not be any suggestion that you should wait in case he was able to change your mind.
So I think the same applies here. If he doesn't want any more children, to the extent he is prepared to take permanent steps to avoid that, then I think you need to respect that. If you want to break up your children's family to pursue your own desire for a baby then that is your choice, but you need to do so with your eyes wide open to the fact that you may not be able to have another baby anyway, and that your existing children will resent you for it when they get older.