We've been over this before, please read the thread.
The question is whether the 22nd Amendment, which prohibits certain persons from being elected as President, makes those same persons "constitutionally ineligible to the office of President" (which would likely be read as "constitutionally ineligible to serve in the office of President.
Whether you agree with the argument or not, and whether you like the argument or not, there's definitely a reasonable argument to be made that from the wording of the 22nd Amendment, from what it DOES and (more importantly) DOES NOT say, said Amendment may be construed to be SOLELY a bar on ELECTION to the office; that it does NOT speak to arrival in the office, and service thereof, gained through the line of Presidential Succession.
Frankly, those who favor a strict interpretation of the Constitution are likely to have trouble on this one.
Thanks for this passage. Somehow, in my perusal (again) of the Constitution yesterday, I missed it. This takes away almost all of the wiggle room I was fearing.
I tend to agree with Luke SkyFreeper, that there still remains a small amount of legalistic opportunity, but I'm pretty confident that the USSC would likely strike it down based on this one passage. Without it, I wouldn't have placed a bet either way.