Democrats on Capitol Hill began a nervous debate Wednesday about the course President Obama has set for their party, with some questioning whether they should emphasize job creation over some of the more ambitious items on the president's agenda.

The conversations came as White House officials insisted that the party's gubernatorial defeats in Virginia and New Jersey had few implications for Obama's standing or for Democratic prospects in the 2010 midterm elections.

But moderate and conservative Democrats took a clear signal from Tuesday's voting, warning that the results prove that independent voters are wary of Obama's far-reaching proposals and mounting spending, as well as the growing federal debt. Liberal lawmakers, meanwhile, said the party's shortcoming came in...