My first thought is that it's completely normal to have some initial "buyer's remorse."
My second thought is that the feeling of buyer's remorse is compounded by post-partum blues.
We didn't even have permanent birth control after my third daughter, but my husband did decide for the both of us (and honestly? rightly so) during that pregnancy that three children was our limit. It still hurt like hell to know that, even though nothing permanent was done. Even though I had a brand new baby that was only days old. The thing is that I did enjoy my baby in spite of my feelings. I was able to reconcile the logic against my emotions. The cons of another pregnancy would have been (and still would be) devastating on my body. The financial issues wouldn't be anything to sneeze at either. That's not to say that if our birth control fails or that if God sees fit to bless us with a baby some other way we wouldn't accept it. We know not to turn away a blessing or a gift.
If the feelings persists and you feel anxious or depressed, or you feel as if you're angry or not yourself, or you start to feel resentful and it goes longer than three months, I would encourage you to see a therapist because at that point baby blues would then be post-partum depression. Mention it at your 6-week check-up to your OB/GYN and you could even get some counseling (short term if this is all it is and you're not prone to anxiety and depression) sooner than waiting to find out if it's PPD.
I'm sorry about what you're going through. I've been through this, and even now at 39 and knowing a pregnancy could disable me completely beyond my current disability, I do still have some lingering sadness that I don't have a fourth. I sometimes feel like someone is missing... but then I think that could be because I had a pregnancy loss before my third daughter. I don't resent my husband though. I resent my Fibromyalgia.