Though many students are liberals on social issues, the economic reality of a weak job market has taken a toll on their loyalties: far fewer 18- to 29-year-olds now identify themselves as Democrats compared with 2008.

“Is the recession, which is hitting young people very hard, doing lasting or permanent damage to what looked like a good Democratic advantage with this age group?” asked Scott Keeter, the director of survey research at the Pew Research Center, a nonpartisan group. “The jury is still out.”

How and whether millions of college students vote will help determine if Republicans win enough seats to retake the House or Senate, overturning the balance of power on Capitol Hill, and with it, Mr. Obama’s agenda. If students tune out and stay home it will also carry a profound message for American society about a generation that seemed so ready, so recently, to grab national politics by the lapels and shake.