Sorry, but putting words in his mouth and saying that it's something that he could have said is lying. The fact is that this is a known fabricated quotation being repeated uncritically; its lineage is partly deciphered here and here. This and other known fake quotes continue to be disseminated on the Internet, and some of the other fakes were included in Sally Kern's "Oklahoma Citizens' Proclamation for Morality" legislative resolution. That resolution was published by The Baptist Messenger with photoshopped signatures from the Governor, Secretary of State, and other officials, even though they didn't actually sign it. Their defense was that "artwork used was from previous editions of the paper," which suggests that they've either done this before, or simply are feigning ignorance of the unethical nature of such a photoshop job.
The billboards showcase quotes from early American leaders like John Adams, James Madison and Benjamin Franklin. Most of the quotes portray a national need for Christian governance.
Others carry the same message but with fictional attribution, as with one billboard citing George Washington for the quote, "It is impossible to rightly govern the world without God and the Bible."
"I don't believe there's a document in Washington's handwriting that has those words in that specific form," Kemple said. "However, if you look at Washington's quotes, including his farewell address, about the place of religion in the political sphere, there's no question he could have said those exact words."
Also see Jon Rowe's blog post, "George Washington on the Bible."
(Hat tip to Pharyngula.)