Ok, that last SFGate article says that Bush gave the speech "Standing in the same spot where President Bill Clinton asserted: 'I did not have sex with that woman, Miss Lewinsky'". That's an interesting thing to add. Reminds me of the Daily Show sketch monday night where it was suggested that maybe adultery is a bigger threat to marriage.
It certainly seems unlikely that a constitutional amendment would pass Congress, most of the polls seem to put support for the amendment at far less than the required two-thirds.
Update: Here are some amusing marriage requirements from the bible: Department of Faith and The Sanctity of Marraige, though that last one may be a stretch as it relies on this bit of biblical incest.