Yeah I know, I'm rather late to the party, but I was just reading yet another Lieberman blog posting, which looked into the lesser committees whose current chaircritters are less senior than Lieberman.
One stood out for me: Indian Affairs. I'll dig deeper over the fold
The current chairman of the Indian Affairs committee is Byron Dorgan (ND). Kent Conrad (ND) also serves, so North Dakota appears over-represented. The East appears under-represented though, with the only member from an Atlantic state is Richard Burr (NC).
Connecticut has the Mohegan and Pequot tribes, both of whom operate large casinos.
And of course he'd get to hang out with his bestest buddy in the whole wide world, committee member John McCain.
It should be possible to sell him on this (it's more than he has any right to expect), and it's not like he'd be a wrench in the wheel there.
I don't see that Joe would change his vote on many issues based on who he's caucusing with, but if keeping him on our side gives us more representation on the committees, that'd be very worthwhile, plus even if it's only a few votes he'd change, that's still a precious few votes.