First, I would think that middle linebacker dominates a measure of consistency for the defense with the Cowboys. If Rolando McClain can at least answer the call for muster, and play the base package, that will influence the Saint running game quite a bit.
That would allow Carter and Justin Durant to be used in most packages. This helps in coverages involving tight ends and running backs that slip out.
The wide receivers can be handled with combinations of Carr, Orlando Scandrick, and yea, Claiborne.
The safeties are good at closing into the box area, so both Church and Wilcox can handle the shorter route demands.
If on the outside, Anthony Spencer can add a half dozen pressures in the game, and both Selvie and Crawford can collapse the outside in relatively effective manner...then I can see a bend but not break being effective against Brees and a pretty fluid offense. There are problems with the New Orleans offensive line, so a tough picture and some pressure should be doable.
The Cowboys have to throw down, although, in all Red Zone opportunities.
On the offensive side, if Doug Free holds his side, then the Cowboys should be able to sustain enough drives to win.
To me, the biggest need is no first half turn-overs by Dallas...and make the Saints earn everything.