When you set the overall payment deadline that means that no payments will be accepted after that point.
But, you can adjust some settings to make different deadlines and scenarios. Check out the Advanced Settings available with each item you are collecting to deal with many of the scenarios that Organizers are thinking about. They include: Late Payment Amount, At The Door Amount, and Expires On ____. Just click on the Advanced Settings link at the bottom right of each pay item to manage these settings.