Another way is to have something game changing happen after turn X. For example, if the players can get to point Y and do action Z by turn X, they win and the monsters surrender. Or, if they don't, they better flee for their lives.
For example, enemy army is coming, infiltrators have thrown open the gates. Players have 5 turns to fight their way into the gate tower and release the portculis. If they do, the infiltrators surrender, knowing that they can't lift the portculis before the players's reinforcements arrive. Or, if the players fail, its suddenly become an n+20 encounter and they had better run.
Or, if they don't, that's a great cliff hanger to leave your players with. "Okay, you failed to close the gate and 3000 angry hobgoblins are pouring through the gate. See you guys next week..." And in the meantime, you can think of some exiting, interesting and feasible set of encounters based on how events turned out... perhaps a skill challenge/series of encounters to fight your way free and back to the keep.
Or, if you want to encourage your group to play faster, state that the X deadline to do something is a particular realtime deadline - so, if they don't do Z before 6:00 as indicated by the DM's watch, then whatever horrible it is they are trying to prevent happens.