Legislative implications for "Birther" scenerio

(disclaimer: I'm agnostic on the question of Obama's place of birth, and I am neither a lawyer nor a constitutional scholar - I just got to thinking after reading about Louisiana HB 561)

So what happens to all the legislation that Obama has signed into law if it is somehow discovered that he's not eligible to serve as President of the United States?  While I think it would be impossible to undo it and all the effects of it, I don't think that would even be necessary, because according to Article I, section 7, clause 2 of the U.S. Constitution:

"..If any Bill shall not be returned by the President within ten Days (Sundays excepted) after it shall have been presented to him, the Same shall be a Law, in like Manner as if he had signed it..."

So it seems to me that even if he is illegitimate, the laws he has signed would remain in effect, having not been vetoed after a 10 day period.  I suppose there could be some argument as to whether the bill had actually been "presented" to the President.

I suppose his many executive orders might be "undone" but given the effect of one of his first executive orders closing down GITMO....

What I think would be more interesting is what about any bills that were vetoed by him.  Since all of his acts would be invalid, seems to me that those bills might actually be legitimate laws.