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“The last two years have presented the NRCC challenges no one could have anticipated. Yet together, against all odds, we persevered and came through the fire stronger,” Mr. Cole said.

Meanwhile, even in victory, Democrats face fights of their own.

The Associated Press reported that Rep. Henry A. Waxman of California will challenge Rep. John D. Dingell of Michigan for the chairmanship of the House Energy and Commerce Committee a powerful post that will oversee energy and environmental legislation.

Democrats also began jockeying to fill a leadership opening in anticipation that Rep. Rahm Emanuel of Illinois, the caucus chairman, would be tapped to be Mr. Obama’s chief of staff.

Likely contenders for the post include Rep. Chris Van Hollen of Maryland, chairman of the Democratic Congressional Campaign Committee, Rep. Xavier Becerra of California, assistant to House Speaker Nancy Pelosi, and Rep. John B. Larson of Connecticut.

• S.A. Miller contributed to this report.