Looks like smothered mate for black with Nc2# and no way for white to prevent it.
Can you draw this position?
Ok, now I see it. Nd1 avoids the smothered mate because the Black Knight is pinned. White plays 2 Ne3 to cover the c2 square. The day is saved!
Edit: I think my lazy eye may have gotten the better of me in regard to seeing the Knight pinned to the King...

Wow, okay, so it's not TOO far outside the usual realms of chess thought...
If you found yourself in this position as white in a live chess game on this site, what would you do?

I would stall until I ran out of time, and claim a draw by insufficient material
Black can still checkmate you, so its not a draw from insufficient material I think.

That's the thing, I think it is a draw by insufficient material. Of course it depends on the rulebook. OTB at a tournament I don't think a TD would let that move fly, but how specific is, say, the USCF rulebook on this? A King and Knight is insufficient mating material, so white's clock running out means a draw rather than a loss for white. Any rule-savvy types out there? Can white just run down the clock? Or, even more audacious, can white simply claim a draw?

Well, black has sufficient material to mate, because in some cases his knight will deliver checkmate (once more, the one knight black has happens to be sufficient to checkmate his opponent), so you definitely can't claim a draw.
The irony is that in this situation white can't claim a draw, but if he had no pieces on the board (just king vs king and knight), he could. In this case the fact that white has more pieces means it is still possible for him to lose because his extra pieces can actually take squares away from his king.
Here's the puzzle: white to move and draw. The puzzle's not perfect; I think there are two solutions. Can you find them both?