Yes. The cage should pivot freely, with a spring to take up that slack; some kinds of lubricant, like 3-in-1 oil and WD40, can dry up into a gummy stuff that slows movement down or even prevents it. If your bike has been sitting unused for a few years, this is likely the case. Work some oil into it --oil it and move it back and forth with your hand-- and it will probably come back to life.
any suggestion as to which oil/lube to use? wd-40?