Let's get the bad stuff out of the way first. This song is really muddy in the low end. It's mainly the fault of the deep piano/strings combo. Take off any reverb/delay/sustain pedal you have down there, the song should really clear up once you do that. Plus I think you have too many instruments down there (though it's hard to tell). Just one - the piano - should be sufficient.
The other thing is that I think you've transcribed the piano of the original song slightly incorrectly. There's no high note being played immediate at the third bar. I think the rhythm of the other notes is also just a touch off (but not enough to really drive me crazy).
The good stuff is that your singing is totally fabulous and it ties the whole song together. I really like the subtle delay that you can sometimes here "suckers luck-uck-uck". I'm not much of a singer, so I can't talk in very technical terms, but you did a really nice job here.
Also, you chose the BEST POSSIBLE SONG to cover. I really like The National and I like this song in particular. So good job there. ;-P