How about pumping in the early morning? I had the same prob as my 6-week old son nurses every 2 hours and my pediatrician suggested I pump one bottle for my husband to do a late evening feed so I could have a longer rest-interval.
He originally suggested that I pump AFTER each feed but my baby is a really efficient nurser and I found it very disheartening to pump so little (literally a few drops). What I now do is that for the early morning feeds (either 3 or 5 am feeds) I will pump the OTHER (full) breast to collect a full bottle. I find that my breasts fill up faster during these times (also b/c I go back to sleep after nursing, which also speeds up the "refill" time) that when he wakes up for the next feed, there is enough for him again.
Sometimes I only manage to fill half a bottle during a pumping session, in which case I will pump again the non-nursing breast the next time I feed (and both breasts are feeling fullish) to fill up the bottle.
(Once you have one full bottle to extend the between-nursing times, I find it's easier to pump a daily bottle after that.)
I also read that you could try pumping BEFORE you feed (but only 20-30 mls) to build up supply as the baby is more efficient at extracting your milk than the pump is. (I think I read it in "Happiest Baby on the Block" by Harvey Karp.) The only prob with that is that you will be collecting only foremilk.
Good luck!