As Project Manager, you have essentially been intrusted with someone else's resources and even their professional future to some degree. This is due to that fact that while you have been made responsible for carrying out the project - they have remained ultimately accountable for the project's outcome.
Combine this reality with the high degree of uncertainty that looms over projects when they are first scoped out and the first project road map is created, and you are in for some tough conversations throughout the projects, as milestones are missed, deadlines need to be extended and additional budgets need to be allocated.
How tough these conversations will be and what will be the severity of their outcomes will be almost entirely reliant on the "customer's" sense of your own sense of ownership and accountability towards this project and in fact towards them. If they walk away from these difficult calls with a strong internal sense of trust in your unwavering commitment to the project's (and their) success, they will be more forgiving, more understanding and even more willing to proactively support your beyond the original scope that was defined.