Third Way, an organization of centrist Democrats, produced a study showing that liberals are the smallest share of the electorate and not enough to keep Congress in Democratic hands. Citing Gallup polling data, the study said self-described conservatives made up 42 percent of the electorate, compared with moderates who make up 35 percent and liberals who make up 20 percent, a shift of several points to the right in the last two years.

In 16 of 21 hotly contested states, Democratic candidates who simply match Mr. Obama’s overall 2008 performance still will not have enough votes to win, according to the group’s study. Instead, the study said, the candidates must outperform Mr. Obama among moderates.

“Even if Democrats close the enthusiasm gap with their base, they still have another enthusiasm gap to close with moderates,” said Anne Kim, domestic policy program director for the group. “Democrats don’t have the luxury of leaning on their base to deliver wins because there simply aren’t enough liberals.”