I really don’t think there are a lot of serious conservative bible scholars who will claim the US Constitution and Declaration were “inspired” in the same way the holy Scriptures were inspired, that is directly by the Holy Spirit.
The doctrine of biblical inspiration—that is, literally “God breathed” is quite different than the idea of high or inspired writing—of other, lesser works. Shakespeare, or Milton, or Plato are surely inspired, but not, without error like the inspiration of the Holy Spirit.
No serious Christian scholar that I know of will claim that the Declaration or Constitution are inspired of the Holy Spirit and inerrant. Washington, Adams, Hamilton, Jefferson or Madison wouldn’t either—which is why the Amendment process is built in.