I have in mind the "you must take the objective by 10.00 hrs otherwise it will be too late" etc mission/orders. So the attacker really has to push on.
Whilst I'm not really a fan of set number of turn games this would, in some rules, be a way of managing this. However, this won't work in CoC as you can have games which, whilst having potentially dozens of phases, may only last a single turn. Maybe this could give impetus to the defender to use CoC Dice to churn through turns but it is too uncertain how many 5's you may get to assure this mechanism will work.
I guess you could set a game time limit i.e. 2-5hours (or whatever) real time to complete the game?
Should the attacker get a support bonus to offset the time pressure?
Any thoughts and suggestions welcome.

Cheers
Nick