I think the caveman wouldn't fare any better :)

There was a (possibly unethical) experiment where scientists tried to induce stress symptoms (lack of appetite, depression, panic, etc.) in rats.

They found that sudden scares or bringing the rats face-to-face with predators had little long term effect. But placing them on a floor with a constant, slightly uncomfortable electric current (low-level stress over a longer period) did cause them to develop all the symptoms.

So perhaps we're just not naturally equipped to deal with permanent time pressure, upcoming appointments and deadlines in the way modern society gives them to us.