Probably not. Although the recession has given us new insights to the question, it has not been serious enough to really test the question. The unemployment of the 1930s depression was in excess of 25%. That's a lot more than our current 8.6% with only 4.4% of college educated unemployed. It's pretty clear, though, that some jobs are more secure than others and there's a simple test to distinguish between secure jobs and jobs that may get outsourced or obliterated.
Alan Blinder, the well-known Princeton economist, argues that the "crucial distinction" in the new labor market is not between those with more or less education. Instead, he concludes that those whose services can be delivered over the internet are in a far less secure position than those whose services must be delivered in person or on site. As Blinder puts it, "you can't hammer a nail over the internet." Nor can Indians who live in India replace your bathroom tile. This model, of course, says a lot for going into the trades, or into many sales positions.
If you're more interested in the cubicle of a major corporation, the distinguishing factor, as I've indicated on numerous occasions, is high quality people skills. The best jobs go more and more to those with a strong functional technology plus solid people skills. Over the years I've watched numerous professionals in all the business functions get sidelined because of inadequate relationship skills. Indeed, the research at the Dallas Fed confirms my observations in spades about the role of people skills.
The good news is that people skills are grown, not born.