Well, it takes me a gradual increase of effort over time to get up near my maximum heart rate. For me, the heart rate sort of lags the effort a bit.

Now it also seems to me that maximum heart rate is exercise specific. In other words, the same person will get different maximum heart rates doing different aerobic activities like running, cycling, rowing etc. Finally, I do not think that maximum heart rate is an indicator of fitness. I did not fool with this when I was out of shape. But my maximum heart rate does not seem to change with fitness level. (I have not done a study on this though). I believe that one's resting heart rate does reflect aerobic fitness though.