The White House may downplay Tuesday's Election Day outcome, but moderate and conservative Democrats in the U.S. Congress say results signal voter uneasiness.

Congressional Democrats point to the number of independent voters who flocked to Republican gubernatorial candidates in Virginia and New Jersey, helping them defeat Democratic candidates. They're warning that results indicate independent voters are wary of President Barack Obama's sweeping proposals, and mounting federal spending and debt, The Washington Post reported Thursday.

"The question is, do people think we're tending to the things they care about?" Sen. John D. Rockefeller IV, D-W.Va., said as he left a Senate leadership meeting Wednesday. He said colleagues were concerned that the main items Democrats pursue -- healthcare and climate change -- don't connect with voters trying to find or keep their jobs.

"Don't think people in my state are going to stand up and start cheering about Copenhagen," Rockefeller said, referring to the U.N. Climate Change Summit in Danish capital in December. Critics of climate change legislation moving through Congress said it would kill jobs in states dependent on manufacturing and natural resources, the Post said.

Steve Elmendorf, a Democratic strategist and a top congressional aide when Democrats lost control of the House in a 1994 GOP landslide, said Wednesday lawmakers are less sanguine now than they were 15 years ago.

"They need to pay attention to it," Elmendorf said. "Voters spoke, and I think the message they sent was they care about the economy and they care about jobs. I don't think there's any reason to panic here. We have to get healthcare done, and then we have to turn our attention to the economy and jobs."