You might want to open up a conversation also on why she thinks that your family can only handle two children. Explore more fully what her issues are, and try to address them.
As a woman, wife, and mother, I can tell you the single most important thing you can do to encourage your wife not to cut off her childbearing ability is to be an active parent once the blessings start arriving. Change diapers, don’t always assume a fussy baby needs to be nursed and hand him back, get up at night, especially when baby is no longer nursing, encourage her to pump a bottle and sleep through a feeding, Enlist a family member to feed/entertain the baby once in a while so you can get through dinner and reconnect, stuff like that. Little things done over and over are HUGE. They will win her over faster than any argument.
**I don’t know if you’ve heard of it, but there is a hilarious book out called “porn for women”, which shows pictures of (clothed) men helping with housework, etc. My favorite photo, my “porn” fix is a picture where in the middle of the night, a couple is in bed,and the man is in the process of getting up, and the caption says “Is that the baby, I’ll get her, you go back to sleep”.
**
It’s that kind of ultra sexy stuff that will get you ABC free lovemaking. Just sayin’
As for public conversations, you can keep it light, and say something like “she doesn’t yet know what an awesome father I’m going to be, or how completely awesome our kids are going to be,” and raise a glass to here’s to hoping she changes her mind.