Agree with Tony. I come from a strong weight lifting background and tried to do both for a while, but it does not work. You run into a few issues, 1st off is time. To be real competative in cycling you really need to get as much time on the bike as possible and need to have good full recovery days (time in the gym is not a full recovery). Currently I am overwhelmed with cycling and life in general, which actually makes it difficult to get good recovery days because on my off days I am cutting the grass or doing other things around the house.
2nd is that when I lifted I gained a lot of mass, all be it you don't have to lift with this focus, but on the bike I need to be as weight efficient as possible. So when I did both I was losing muscle mass no matter how hard I lifted or how much I ate and was not performing at my peak performance on the bike because I was tired and weighted more than I should.
I stopped lifting last November and went from 225lbs to 185lbs, I am leaner, faster, and much more efficient on the bike. I feel like I am in the best shape of my life, far better shape than I ever did during my 10yr lifting stint. My racing season is going great.
I am not saying that I don't do some pushups and situps every once and a while or throw in the P90x video, but those things only happen if I feel like I have some energy and time to expend.