This is my first tab but I think it's nearly right. And excuse me for my bad English.
To play this song, in the video, Jay Brannan seems to have tuned his guitar one full 
higher than standard tunning and to have the capo in the 2nd fret...
The chords are these: Bm F# G A
And they are repeated all along the song.
The same hand position is used for every chord:
Bm: 2 2 4 4 3 2
F#: 2 4 4 3 2 2
G:  3 5 5 4 3 3
A:  5 7 7 6 5 5

I think this is the way Jay Brannan plays it:
 Bm            F#            G             A
--------------------------------------------------------|
-------3-------------0---------------------------0------|
---4-----4-------------3-----------4---------------6----|
-----4-----4-----4-------4-----5-----5-------7----------|
-2-----------2-----4-------4-----5-----5-------7--------|
---------------2-------------3-----------3-5------------|


***
This sounds can also be played using the standard G and A chords, what for me is easier. 
doesn't sound exactly the same because there are more open strings but I think they can 
for beginers like me.
My version:
G : 3 2 0 0 0 3
A: 0 0 2 2 2 0

--------------------------------------------------------|
-------3-------------0-------------0------------0-2-----|
---4-----4-------------3-------0-----0------2-----------|
-----4-----4-----4-------4-------0-----0------2---------|
-2-----------2-----4-------4--------------0-------------|
---------------2-------------3----------3---------------|
***

This is repeated most of the song, with some small arranges but I'm sure you can figure 
out.
This happens until before "Zeus was afraid of his girlfriend..."
From where the same chords are played but strummed.

And finally in the last part only the first string of each chord is played:
--------------------------------------------------------|
--------------------------------------------------------|
--------------------------------------------------------|
--------------------------------------------------------|
-2------------------------------------------------------|
---------------2-------------3------------5-----5--5----|


That was all. Enjoy.
And thanks to Jay Brannan for all these great songs, so simple as brilliant.