It sounds like they need more than one project manager and a number of additional worker-bees to get the jobs done.
There are three responses that might generate:
* "you'll just have to work harder" This response is not unusual but tells you you're going to fail anyway and is a signal to get out of the organization before it crashes and burns.
* they'll cancel some projects and focus their people on the remaining ones
* they'll hire some more warm bodies to get more work done.
My recent favorite response: "I reject your linear thinking. You are much smarter than I about how to find technical solutions"
Although it's clear I'm not smarter than him as I hadn't considered leveraging non-linear causality to complete technology projects on-time