'A consensus guy'
"We have had a long-standing good relationship. I have found him to be a consensus guy," said Senate Democratic leader Harry Reid, who survived a tough re-election fight in Nevada.
Reid told reporters that Boehner's statements since the election sounded like "the John Boehner that I know, somebody willing to work with us."
Jockeying for congressional leadership has begun. Pelosi was silent about whether she might step down from her leadership post or resign from Congress. The House's No. 2 Democrat, Steny Hoyer of Maryland, is seen as a possible successor.
Republican Representative Mike Pence resigned as conference chairman amid speculation he would mount a presidential bid.
In the Senate, Republicans gained six Democratic seats -- in Indiana, Wisconsin, North Dakota, Pennsylvania and Arkansas as well as Obama's former seat in Illinois. The Senate race in Washington was too close to call.
The three-way race for the Republican-held Alaska Senate seat also was close, with incumbent Lisa Murkowski running as an independent write-in candidate against Tea Party favorite Joe Miller and Democratic challenger Scott McAdams.
The Republican rout extended to governors' races, where they picked up at least 10 governorships from Democrats, including the battleground state of Ohio. They also seized control of at least 17 state legislatures from Democrats.