He’s already served eight years. Being elected VP would expose him to the possibility of twelve years in the Oval Office, falling afoul of Amendment 22.
From my understanding, he could still be President because the 22nd Amendment would only prevent him from running more than 2 elections OR seeking election if he were to become President during someone else’s term for a period more than 2 years.
This is not a settled question. Since we have yet to see a former President seek to be Vice Pres. after being elected to 2 terms it is still an unsettled area of law.
He’s served over half of two terms as President. That makes him ineligible for the Presidency. And being ineligible for the Presidency, in turn, makes him ineligible for the Vice Presidency, as well. There are a few quibbles that can be made in this, but no court would ever support them.
For the record, here is the text of the 22nd Amendment:
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No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once. But this Article shall not apply to any person holding the office of President, when this Article was proposed by the Congress, and shall not prevent any person who may be holding the office of President, or acting as President, during the term within which this Article becomes operative from holding the office of President or acting as President during the remainder of such term.
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This article shall be inoperative unless it shall have been ratified as an amendment to the Constitution by the legislatures of three-fourths of the several States within seven years from the date of its submission to the States by the Congress.
The text says no person shall be elected to the office, not no person shall serve as President. And it says nothing about a former Pres being elected as VP either.
Since the Vice President’s only substantial constitutional job is to swoop in if POTUS dies ro is incapacitated, why would you want one who couldn’t do that?
To cast tie-breaking votes in the Senate. Besides, the VP has important non-Constitutional jobs, including helping the President lobby Congress and to help use the bully pulpit of the Vice Presidency to sway public opinion, and to offer the President different options, assist with administration, and other duties. I grant you that it would probably be unwise to select a VP who can’t ascend to the Presidency because the President has no control over who the Speaker of the House is, but Dick Cheney was an extremely effective and powerful VP without ever exercising his Constitutional powers. Without getting political, Dick Cheney successfully implemented many of his own views and the Republican Party’s policy goals by using his position as the VP.
He CAN do that. He can’t be elected president.
Let’s say a former President decides to stay active in politics and wants to run as a Congressional Representative. You think that wouldn’t be allowed because he might be in line of succession? Or his colleagues can’t elect him Speaker for the same reason? Or he can’t be appointed to a Cabinet position for the same reason?
Ahem.
[QUOTE=Let’s say James Madison, as it’s the Constitution. The bolding’s all Skaldimus, though]
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
[/QUOTE]
Do you see the word elected above? Because I don’t. I see the word eligible.
Who cares?
The VP has three constitutional jobs: to take over if POTUS is dead or incapacitated, to preside over the Senate; and to break ties in the Senate. The first one is clearly primary; the second one is only pro forma at this point; and the third one is rare (though not as rare as taking over the Oval Office). I see no point in anyone choosing a running mate who couldn’t do the primary function.
I realize that Cheney (and also Gore) took on a lot of other duties. But the VP’s other jobs are at the pleasure of the president. There’s nothing about them that couldn’t be assigned to the chief of staff or secretary of {insert cabinet department} or another high-ranking federal officer. It’s all about who the president puts his or her confidence in.
Ahem.
To revisit the language of the 22nd amendment.
That doesn’t supersede the section of Article II which I quoted; it just adds an additional qualifier.
We as a nation could have chosen to amend Article 2, Section 1 of the constitution to change the eligibility requirements. But we didn’t – they remain unchanged.
Or we could have written the 22nd Amendment to say that a two term president is no longer eligible to be president. But we didn’t do that either. The language says a two term president can no longer be elected president.
Surely people understand that election is not the only route to be president. Yet the 22nd Amendment precludes just the single route of election. I must assume this is deliberate.
And I must assume that the framers of the 22nd amendment considered it obvious that what they intended was for such a person to be ineligible for the office, and that they didn’t expect this level of nitpicking.
After 150 years of nitpicking the constitution word by word, they wouldn’t expect more nitpicking on new stuff?
If it’s Bachmann, they’ll lose so early, we’ll know the winner before the polls close. 
Why not Herman Cain? Isn’t it sort of expected that bigo-- erm, I mean republicans to show up to the Dems? “Hey, we got a black guy too, and he knows economics! And his middle name isn’t Huessin!”
I have just read the text of the 22nd Amendment, and I note that it does not mention Article II nor say that any part of it is nullfied. This distinguishes it from, say, the 21st Amendment (ending Prohibition), which explicitly calls out the 18th Amendment and tells it to clean out its desk and go home.
Amendment 22 does not undo Article II’s definition of who is eligible to be president; it merely narrows the field on who may be elected president. To claim otherwise is pointless and insupportable.