This sounds like management doesn't know their jobs. Context switching is very expensive and they are effectively slowing down all projects. It would be better

This sounds like management doesn't know their jobs. Context switching is very expensive and they are effectively slowing down all projects. It would be better to just split the developers between the projects and then come up with a more realistic timeline. If that is not acceptable, then cut down on the features to the bone. If still unhappy, well...