I think it would be detrimental to Obama to attempt to use the 14th to bypass congress. It will of course end up in the SC, and could very well lead to his impeachment, depending on their interpretation.
The debt discussed in the 14th is Civil War debt. It is not a discussion of debt in general and does not modify Article I Section 8.
Shall I quote the 14th for you too?
I can tell you see this purely in a black and white sense.
Can Obama Extend the Debt Ceiling on His Own? by Ronald Dworkin | NYRblog | The New York Review of Books
"The debt shall not be questioned clause was added to the Fourteenth Amendment for a specific and immediate purpose: to prevent the new Southern members of Congress, should they gain a majority, from cancelling the debt the Union had incurred in the war. But constitutional interpretation is not a catalogue of historical anecdotes; it is a matter of principle and we are therefore required to identify the principle on which the authors of the clause had to rely. As Chief Justice Hughes said of the clause in 1935, speaking for a unanimous Supreme Court, While this provision was undoubtedly inspired by the desire to put beyond question the obligations of the government issued during the Civil War, its language indicates a broader connotation. We regard it as confirmatory of a fundamental principle
The general contours of that fundamental principle seem clear enough. Congress does not have authority, even by a substantial majority, to dishonor the nation by repudiating outstanding debts it has authorized the nation to incur. The fiscal integrity of the United States is sacred and requires constitutional protection.
However, it's grey enough that constitutional scholars, which I am not, are debating it. The only way the question could truly be answered would be for Obama to try it, and for it to go to the SC.