WASHINGTON — President Obama will again face a divided Congress, as the Republican Party on Tuesday held onto its strong majority in the House of Representatives and Democrats increased their advantage in the US Senate.

From the Midwest, where Democrats beat back energetic challenges from some conservative Tea Party favorites in Missouri and Indiana, to Virginia, where Tim Kaine, former governor, ousted George Allen, former governor and senator, to keep the seat in the blue column, the outlines of the 113th Congress took shape as voters cast ballots in what some election officials said appeared to be record numbers.