Following up on dragonchild
, the best way you can demonstrate this up front is with a detailed project plan. The advanced project manager types use software to designate tasks with explicit dependencies on each other. Then, they schedule the project and it shows the parallel and sequential tasks. If all you have remaining are sequential tasks, more people won't help. If you have a bunch of parallel tasks, bodies might help.
You still run into the issues mentioned above bringing a new person up to speed, but with parallel tasks there is at least the possibility that they can help move things along. If you have a bunch of components dependent on each other, it really won't matter and your project plan can prove it.
If they insist, the next step is to re-design things to remove hard dependencies. But if I remember, Brooks notes that mocking up interfaces to allow people to work in parallel can create some nasty integration problems at the end when people arrive at different points.