It's certainly possible. I haven't been in the dating game in a long time, and of course, objectively I'm a catch (/sarcasm for the internet).
I generally fall into the category of figuring out what's wrong with myself first and then working outward. And in that hierarchy, I'm going to focus on guys before I focus on women.
I guess I can bring up a point in another thread I made -- the idea of de-centering sex and relationships. We place way to much emphasis, and self worth, on whether we can get laid, or end up in a long term marriage. And I say that as someone who enjoys sex and my marriage. But I've gotten happier in my life and my marriage the more I define my value on how well I help other people out, or other measures of my worth to myself and society - and not on how easy it is for me to get laid.