No Deism in the Declaration
It is often claimed by liberals that the God mentioned in the Declaration of Independence is the God of deism. To see that this claim is false, it suffices to read the document all the way through. In the final paragraph we find references to "the Supreme Judge of the World. . . ," and, in the closing lines, to "a firm reliance on the Protection of Divine Providence. . . ."
A God who judges the world and provides for it and its inhabitants is more that a mere cosmic starter-upper. Providence (from L. pro-videre) implies (i) divine foresight, and (ii) the supplying of the world's needs. Neither of these characteristics is consistent with a notion of God according to which God merely causes the beginning to exist of the world and thereafter has nothing to do with it.
Of course, showing that the God of the Declaration is non-deistic does not suffice to show that it is the specifically Christian God. Among other things, the Christian God is triune; but there is no trinitarianism in the Declaration. Nevertheless, showing that the God of the Declaration is non-deistic does lend considerable support to the notion that the God of the Declaration is the Judeo-Christian God, where this latter conception abstracts from the differences that divide Christians and Jews while preserving central common tenets.
There is more on this topic here.