The size of the pot up for grabs should play a definite role in your poker playing. There are several reasons for this, one of which has to do with the fact that it is better to win one extremely large hand rather than a bunch of small ones. Think about it this way, would you rather win $100 one time or $10 nine times? Sure with the latter you would be winning more hands and probably be a bit less frustrated, but the $100 is a larger amount. We play poker to win money, not to win hands.
So if the pot is large, you need to try harder to win it. This does not mean chasing bad hands all the way to the end of a hand. It means intelligently strategizing so that if you do have a strong hand, you are maximizing the amount that goes into that pot. A big pot should be played aggressively, if only for the reason that others will be playing aggressively as well.
If the pot is very big, you will want to try and win it immediately. The more chances you give your opponents to outdraw you the more times over the course of your playing career you will lose those big pots. So even if you think you have the second best hand, you will want to play more aggressively to try and win the pot right away.
If you have the absolute nuts, meaning there is no possibility that your hand can lose, you may want to contemplate slow playing. This is strategy is the exact opposite of the one outlined above. You will want to mask the strength of your hand so that your opponent thinks that they have you beat. This will encourage them to play their hands too aggressively and put even more money into the pot. It does need to be reiterated that this play only will be successful over the long term if you cannot be beaten. If you have any possibility of losing the hand, you will want to win big pots as quickly as possible.