Odds of Getting In
We'll give it to you straight: becoming a mechanical engineer will be pretty difficult. Not only is it tough to make it through an engineering program with all of those math and science classes you'll have to do your best to ace, you're also up against a declining market.
You won't have an unlimited amount of industry positions to choose from, but rather you'll probably just have to pick the one that's most available. So, while your odds of getting in aren't bleak, they're far from great these days (source).