There are, of course, several ways to interpret her remarks and how they reflect on her and the Tea Party movement in general. Maybe she's just an ignorant fool and her ascendency to a Republican Senate nomination is a fluke. Maybe she knows the Constitution decently well, and just got her numbers mixed up. Naturally I suspect that her problem, and the Tea Party's problems, with Constitutional interpretation, are far more substantial.
It's not merely that the movement, at its worst, tends toward "ignorant, know-nothing Yahooism." Beyond that, even the intellectually credible aspects of Tea Party conservatism manifest an ignorance of the history and evolution of the Constitution that, while certainly less farcical, is no less dangerous. Tea Partiers wax poetic about the importance of the Founding Fathers and the original intent of the Constitution in their calls (feigned or honest?) to curb federal spending and reduce the size and scope of the federal government. But in addition to conveniently distorting those founding principles to fit their various ideologies, they also ignore the transformational changes made to the Constitution during Reconstruction [not to mention the economic consequences of fiscal conservatism in the Depression]. The 14th Amendment (was supposed to) fundamentally re-apportion political power between the states and federal government, shifting the burden of protecting people's liberties from the states to the feds. When the Constitution was written, most people assumed the federal government would be the biggest threat to individual liberty, and the states would be its best defender; the 14th Amendment was our collective acknowledgment that we had it backwards. It was a reflection of the fact that the states failed spectacularly at protecting minority rights, and thus was a fundamental restructuring of American government. In their misinterpretation of history the Tea Partiers are certainly not alone; Southern governments and the Supreme Court --with the help of all-around apathy--effectively nullified Reconstruction for generations (a tradition continued today by Justice Thomas et. al), but at least the likes of Thomas can muster some sort of justification for his views. Christine O'Donnell doesn't even know what the 14th Amendment is.
There's a reasonable political debate to be had about reducing the size and power of the federal government; indeed, the prospect of a Senator O'Donnell is perhaps her own best argument for said reduction. But how can we have that debate when one of the relevant parties doesn't know what it's talking about? Even the debate moderator in the video tells O'Donnell the 14th Amendment "guarantees citizenship." Umm, yeah, that and like a whole lot more. What about equal protection, due process, privileges and immunities, incorporating the Bill of Rights, etc. etc?
Even Chris Coons, in repeating the Establishment Clause from the 1st Amendment over and over (or his slightly modified version), probably should have mentioned to O'Donnell that just because it says "Congress," the Establishment Clause applies to the states as well because of the 14th Amendment.
Okay, O'Donnell is a convenient straw man for this argument. She's obviously not the brightest. But her brand of Constitutional literalism (the words "separation of Church and State" aren't in the 1st Amendment....BAM!) combined with its misreading of history is scary, 'cause a lot of people seem to be playing along to the same general tune. Her misreading of the 1st Amendment is absurd. But her ignoring the 14th is far more common and just as troubling.