Of course the first part of the quote can't be refuted. But that's because it's tautological.
It's just another way of saying, "We have the government that we have." regardless of what caused it.
You could replace the word "Constitution" with anything, and it would still be an irrefutable claim.
- The big bang either caused the government we had, or was powerless to prevent it.
- Bert and Ernie either caused the government we have or were powerless to prevent it.
- The antifederalists either caused the government we have or were powerless to prevent it.
- Lysander Spooner either caused the government we have or was powerless to prevent it.
- And so on.
The problem is with Spooner's conclusion. It doesn't follow from the tautological premise that the Constitution (or Bert and Ernie, or Lysander Spooner, etc.) is unfit to exist.
Edit: For the record, I'm not a huge fan of the Constitution. I just don't really care for that Spooner quote either.