The culture of the company plays a major role in how you handle this.
I have worked for companies that run the gamut from demanding impossible tight schedules, to rules that limit how much of any one persons time can be dedicated to the project.
Start with the goals and measureables that you have with your manager.
Then, have a philosophical discussion with your manager.
Next, how well do you know the work habbits and skills of your staff.
How reliable are the target dates for work from other departments that affect your project.
You need to weigh all of the above factors versus the company goals, and critical milestone dates for the project.
Perhaps the most important aspect is contingency plans, and comminication of slippages. Especially when resources that are not in your control are involved.
Chas