I will soon be graduating with my PhD in mathematics, and my experience thus far as a graduate student in the US is that it's really hard to get a position in academia where your research is more important than your teaching, and it's almost impossible to get an industry job where you can research what interests you instead of what's immediately applicable to your company.
I won't have any trouble getting a job. I won't even have trouble getting a very well-paying job. But getting a job that lets me pursue my research interests as I see fit? Not without 2 - 5 more years of postdoc positions and some really great papers. And then 5 more years of writing papers like a maniac to get tenure. A lot of pressure to go after low-hanging fruit, even if it's stuff that doesn't interest you. That's a lot of years of 80 hour weeks just for the privilege of studying what you want.