The nice thing is that they had to have at least 9 of the 13 states ratify via convention, not via state legislature. The document had been published, and then it became necessary to elect delegates to ratifying conventions and have them debate ratifying it.
So it had been nailed to the tree for quite a while, but that did not stop the proponents of the Constitution from demanding quick action. You'll see that in two weeks when Federalist #1 comes up for the book club.