Several sources attribute this quote to George Washington:
True religion affords government its surest support. The future of this nation depends on the Christian training of our youth. It is impossible to govern without the Bible.
For example:
Did George Washington say this?
No.
It is very hard to prove someone did not say something.
The etymologist users at Wikiquote have declared this as misattributed.
It is impossible to rightfully govern the world without God and the Bible.
Wrongly attributed to George Washington; while he is known to have made some official statements of public piety, this was not one of them; it is sometimes wrongly cited as having been in various official statements, but the earliest attribution of the remark yet located is one which cites no sources in Upper Room Bulletin, Vol. 7, No. 3 (23 October 1920).
Note: Wikiquote isn't a very strong reference to support this. They do link to the 1920 quote, but that isn't proof that it isn't older.
Meanwhile, the Fake History blog tracks several different variants - e.g. an 1835 biographer who claimed Washington said:
It is impossible to govern the universe without the aid of a Supreme Being.
By 1867, that had transmorphed into:
It is impossible to govern the world without God
While this isn't hard proof that Washington did not say the exact phrase given, it is reasonable to accept that this is a different quote from Washington that has been corrupted in the re-tellings.
The first part of the quotation, namely "True religion affords government its surest support" is genuine. It is repeating a statement made to Washington by the Synod of the Dutch Reformed Church in North America in 1789.
Washington's reply included:
You, Gentlemen, act the part of pious Christians and good citizens by your prayers and exertions to preserve that harmony and good will towards men which must be the basis of every political establishment; and I readily join with you that “while just government protects all in their religious rights, true religion affords to government its surest support.”
