My honest opinion is to let him go ahead and have the procedure. It isn't just economics that prompt me to say that, although certainly that is a concern. The main reason is that he doesn't want another child.
It is one thing to want another child and not get one, but it's quite a different matter to NOT want another one and get one anyway. Resentment can grow very quickly in that case. First, your husband will resent you for doing it against his will (although it takes 2 to make a baby, being dishonest about birth control will really make him mad), and for another thing, you risk making him resent any new child that comes along. Do you really want a child to go through life knowing his or her father resents the very fact that he or she is in the world? I wouldn't want that for any child of mine.
Sure, you think he will get used to it and grow to love the child, and that may or may not be true, but either way, he will lose his trust in you, and you probably don't want that.
My feeling is that you have already been blessed with 2 wonderful children. You should count your blessings and spread your love between them and your husband. I know it would seem like 3 would be normal for you, but that is just a number. 2 parents and 2 children can be just right.
Now, if you and your husband agree together to let him get his procedure and have no more children, you might think about taking the money you would have spent on another child, and banking it each month towards your two existing children's college, or perhaps your retirement account(s). Diapers, formula, baby food, wipes, car seats, swings, burp pads, clothing, doctor visits, emergency room visits, hospital stays, c-section out of pocket costs if that is a concern...all of those things really add up to a whole heck of a lot of money, even if you already have some items there from your other two. Add it all up into a yearly cost, divide it by 12 months, and that is how much money you can save by NOT having another child. Further divide it by how many paychecks you and he get each month, and then bank that amount each paycheck (or put it into your IRA, however you want).
Obviously, there is no one giving you advice who is really going to know exactly how YOU feel about this, but then again, you might not know exactly how strongly your husband feels against the idea of another child. I wouldn't risk my marriage and future happiness when you already have two blessings.