The only thing you can do is look at past recent history. During the last big recession – the one in the late 1980s, early 1990s – more people went back to school at all levels, and far more people applied to graduate and professional schools after completing their bachelors than normally would have.
I don’t have all the data yet, as it’s still a bit early, but from what I can see so far, the only two growth areas we’re seeing right now, at this moment, in terms of the US economy are in healthcare and in education.
I suspect, based on all that, that yes, more people may be applying to med school than might, normally, do so. However, I think the major competition will come at things like nursing progams. Med school may be a bit less impacted than other health-related programs, because to even be able to apply to med school, one needs to have prepared, and that prep takes a long time, and isn’t easy. So while I think the number of med school apps will go up, it won’t be by some huge amount. More likely, more kids will try to be pre-med – and not succeed. More likely, more kids will try to get into the medical fields that require less prep and expense than med school, such as PA and nursing.
The professional schools where I think there will be a significant increase in apps are law and MBA. That’s because those can be lucrative, like medicine, and can make you more marketable – but one needn’t have done any specific coursework in undergrad in order to apply.

It shouldn’t. I just accepted into Graduate school last week for a Masters of Arts. I was worried about my chances too, but the recession has no affect on it really. Med school is competitive no matter the economy. Cause if you have a premed degree, you really cant do anything with that and basically have to go into Med school. If your qualified, you are good. Good luck with it. I have been there with the questioning.