I can't say I agree with the women who say "just don't do anything for a weekend and let him see what it's like." My husband has a much greater tolerance for mess/dirty laundry/etc than I do and it would just drive me crazy. Plus it doesn't do anything to help your resentment.
I have this same issue with my husband (but we're working on it), and here's what's working for us. Start by making a list (maybe start small - only one or two things) of things that are his responsibility. Be very specific (don't say "pick up around the house"; instead say "put all your dirty clothes in the laundry room hamper") AND (and this is key for me and DH) set a "to do by" limit (ex. by Wednesday evening).
It turned out that my DH and I had different ideas of how "urgent" different chores were. I would ask him to put away his laundry, and he figured he'd get to it when he got to it. I wanted him to do it RIGHT NOW, and he would rather finish his video game, send some emails, whatever, and THEN put away his laundry.
He felt I was "nagging" when I asked him to do something while he was in the middle of something "just as important" (even if it was "only" a video game or talking on the phone). I would have just multi-tasked and done "x" while talking on the phone, but he likes to do things one at a time. So, for us, it sets reasonable expectations for the both of us if I say "DH, please take out the trash before you go to bed this evening." Then, he can do it as his leisure, and he knows that I have an expectation of something getting done.
It doesn't always work out, but it's been a good starting point for us.