It is important to warn the curator as early as possible and find solutions to the situation with him/her. Maybe you can postpone the deadlines, or you can invite someone to help, or transfer the task to another person.
The main thing is not to be silent, not to delay until the last moment, when the deadlines are already on fire. Everyone may have unforeseen circumstances, workload, etc., which will prevent them from completing the task on time. This is normal.
Just warn the curator so as not to let the team down.