It can happen. Sometimes, you can do everything right and not get any results.
I've had odd jobs since high school, but not any jobs aside from unpaid internships in my area of expertise, which is engineering. When I graduated from a university which was in the top 20 in the country (top 10% in my class, no less), I sent out over a hundred resumes, but that was during the economic downturn, and I got less than 10 offers for interviews, and no resulting job offers. Instead, the jobs either went overseas or to minorities who clearly weren't qualified (I say this because I know some of the people who were hired at some of these companies).
I ended up working as an auto mechanic and a furniture mover for a year.
After that, I decided to go abroad, and I taught English for two years in Asia. This wasn't some crappy gig in some off-the-map town. I was teaching in one of the top-rated private schools in that particular country. When I left, a government official wrote my recommendation letter, as I had taught his son. After that, I went to England and got a Master's at Cambridge in my field, published papers, attended conferences, the whole nine yards. Came back to the states in late 2010. Everywhere I apply to either turns me down, or if it's a place like WalMart or McDonald's, says I'm overqualified.