Republicans have, so far, not been willing to use the "big government" label to attack anything to do with military, police, or espionage - their "law and order" platform trumps their "small government" one.
In the bizarre logic of American politics, Republicans and Democrats are both pro-NSA, while the Greens and Libertarians are anti-NSA.
That's why I said "potential". Depending on how the wind blows, the small-gov platform could give them an easy angle, and if it doesn't, they're still the party of law and order, so it's a win-win. Dems have a harder job, for them it's a wedge issue.
In the bizarre logic of American politics, Republicans and Democrats are both pro-NSA, while the Greens and Libertarians are anti-NSA.