Any plan based on secrecy will fail.
If even one person knows about it, Santa knows about it, right?
Any plan based on overpowering Santa will fail.
If a surprise attack won't work, then an attack so powerful that Santa can't prevent it seems like the best alternative. However, there is a small problem with this: how do you capture someone who not only can move a 350,000 ton load at a speed of 650 miles per second, but also has a demonstrable ability to enter and exit locked, secured buildings without even leaving a sign of forced entry?
I think it is safe to say that no military force would be able to cope with these abilities. Even a sky filled with drones would be completely powerless to stop an object moving at this speed. Forgetting the first objection above, even if you could launch a surprise attack, Santa almost certainly could simply escape from any ambush without being captured. He could probably even come back to the site of the ambush, deliver presents, eat cookies, and then leave again without ever being threatened.
The best bet is to use threats to secure Santa's cooperation.
The NSA could threaten to do something really bad unless Santa helps them out. It is clear that Santa has a strong preference for goodness over badness and wants to help people, and the NSA could probably take advantage of that to get him to voluntarily agree to cooperate with them. There is no need to speculate what they should threaten; there are many possibilities, and they could try various threats until they find what works.
Could Santa stop the NSA from doing the bad stuff? It seems unlikely, since lots of stuff that Santa doesn't like already happens in the world, and he other does not or cannot use his Christmas magic to stop it.
Could Santa expose the NSA's plan? He could only do this at great cost to himself. He would have to:
- Announce his existence to the world.
- Demonstrate his magic powers to prove his identity (otherwise he would not be a credible witness).
It is possible that Santa would think this is worth it, given the circumstances. However, it is equally possible that he fears that the consequences of such actions would be much worse than cooperating with the NSA. If he reveals himself to the world, it would lead to all of the crazy, evil people in the world trying to capture him and use his power to their advantage. They know how to find him. While he might not be catchable, it would probably put an end to the whole present-delivery thing. So I think there is a good chance that he would give in to the NSA's threats and cooperate.
Addendum: why the NSA should worry about their plan.
Santa's non-intervention in most world affairs, despite being a deep philosophical conundrum, should raise some concerns in the NSA. Why doesn't Santa replace all the guns in Syria with teddy bears overnight? Why doesn't he airlift food to starving populations? Why doesn't he voluntarily share at least some intelligence (if not with NSA then with others he trusts more) to stop bad things from happening? Actions such as these seem easily within his capabilities, and they also seem to do much more good than the comparatively trivial act of distributing toys yearly.
I see two main possibilities here:
- Santa doesn't intervene for philosophical/ideological/moral reasons. He follows a code that requires him to only do Christmas, and not participate in world affairs otherwise. This is problematic, as it appears to make Santa into a moral monster. However, it could be possibly justified philosophically. Perhaps Santa believes that all of these other interventions, while seemingly good, would actually do harm in the long run. Call it the "add toys to make it the best of all possible worlds" theory. In this case the NSA should worry, since Santa might choose not to intervene to stop the bad stuff they threaten. However, he might be responsive to threats to disrupt Christmas.
- Santa's power only applies in limited circumstances. The magic doesn't work for everything, but has some limitations that make it impractical to apply to non-Christmas-y objectives. In this case, the NSA should worry that Santa might not even be able to help them. However, there are possible sets of limitations that would prevent Santa from intervening in world affairs generally, but still leave him able to share intel with the NSA. Any limitations to Santa's powers also create some new possibilities for capturing him, so the NSA should research this fully before proceeding.