I am ignorant, speculating, and asking for information. I am a bit puzzled by self proclaimed constitutional conservatives enthusiasm for the Declaration of Independence. I always consider the Declaration to be the lefty document and the Constitution to be a sharp shift right.
My guess is that they mainly interested in one word in the Declaration "creator". OK also "the Supreme Judge of the world" and "divine Providence"
They also consider themselves Jeffersonian which is odd, since he is the only major party presidential candidate to refuse to publicly declare himself a Christian (and in private correspondence said he was a Christian only if belief in implausible claims such as the virginity of Mary was optional "And the day will come when the mystical generation of Jesus, by the supreme being as his father in the womb of a virgin will be classed with the fable of the generation of Minerva in the brain of Jupiter" http://www.beliefnet.com/resourcelib/docs/53/Letter_from_Thomas_Jefferson_to_John_Adams_1.html Jefferson, of course, was no more an atheist that Robespierre was (although he believed in freedom of concience, tolerated atheists and didn't sentence atheists to death as Robespierre did)).
I note that the Declaration was amended by Congress. The working document is here with a transcription
from Jefferson's draft "We hold these truths to be sacred & undeniable; that all Men are created equal & independent; that from that equal creation"
no "creator" similarly the draft contains no reference to any "supreme judge" and no reference to anything "divine" anything (search to check)
http://www.ushistory.org/declaration/document/rough.htm
Of course Jefferson was one person and Congress had the authority to ignore his draft entirely (or vote down the resolution to be independent).