So I'm friends with Spain. She says she wants to go to war with England. I say give me 10 turns to stall her. I don't really want to fight England right now, but I don't want to make her 'unfriend' me. When 10 turns are up, is there any impact to telling Spain 'Sorry, I changed my mind'?
It is possible to change your mind. When they prompt you to start the war, you will have the option to say that you changed your mind. If you do this, you will lose influence with them, which can be seen in one of the details you see when you roll over their name as "You said you would go to war with them, but then refused." in red.
Also worth noting is that declining to join them in war initially does not have any effect on your diplomacy with them.