Most companies or organizations have multiple projects all pulling at resources to achieve their goals.
It is important that the program or projects manager be aware of what each projects status is and what the priorities need to be. These priorities should be managed and communicated with the department heads and project managers so that people are aware of where resources are needed most and where they should be allocated based on the overall goals (not just the goal of each individual project).
It is also up to the individual project managers to forecast what resources they will need so that proper planning of resource allocation can be done by management.
The ultimate priorities need to account for things such as late fees, penalties, the image of the organization, client satisfaction etc.
If proper planning and resource forecasting is done, there should not be a problem with multiple projects pulling at scarce resources (which leads to internal conflicts).