Taken from the archives of "Dear Prudence" at Slate.com, Prudence offers Remorseful Job Applicant great advice:
I've been out of work for several months and have had trouble landing interviews—I have children and really need a job. My résumé is fantastic, with excellent references, but I do not have a four-year college degree. Finally, I got desperate and edited one of my résumés to show that I had a bachelor's degree from a college I attended 30 years ago. I sent it out only once (and have since deep-sixed it). The problem is that I received an inside referral to a job with an excellent company, hit it off with everyone during the interviews, and landed the job—contingent on my passing a background check. This is where I sent my falsified résumé. I completed the background check truthfully. But now my stomach is churning and I want to call the company, tell them what happened, and resign the position. I've never done anything like this before. It may be the worst thing I've ever done in my life.
—Remorseful Job Applicant
Do not resign! Contact human resources immediately and tell them there's a mistake on your résumé and that it should say you attended, not graduated from, your college. Let them know the background-check form is accurate. That may take care of the problem. If your call raises questions, be succinct and truthful. Say you made this onetime mistake in a foolish attempt to improve your résumé, you regretted it the moment you did it, and whatever else happens, you are relieved to have put things right. It's much better for you to come forward first before the checkers find the discrepancy. Yes, there's a chance they won't, but that's a big risk. If they miss it, and you do get hired, every time anyone says, "Marvin, can I see you in my office?" your stomach acid will pour. If you get the job and this comes out later, it could be a firing offense. And if this is the worst thing you've ever done, take pride in having led such an exemplary life.