"I think there's the urgency of the matter that probably goes beyond anything we've seen to date," he said. "The urgency of the repercussions of driving off the cliff are so grave that I can't imagine that failure is an option."
Both Biden and Reid pointed to election exit poll results showing that most Americans support higher taxes on the wealthy.
Biden said there was "a clear sort of mandate about people coming much closer to our view about how to deal with tax policy," adding that "there's all kinds of potential to be able to reach a rational, principled compromise."
Boehner, for his part, said that for Obama to get support for new revenues "the president must be willing to reduce spending and shore up the entitlement programs that are the primary drivers of our debt."
"We aren't seeking to impose our will on the president. We're asking him to make good on his 'balanced' approach," the Ohio Republican said on Capitol Hill.
The reference to a balanced approach to deficit reduction reflected Obama's campaign-long call for higher taxes on incomes above $200,000 for individuals and $250,000 for couples. That was something Boehner made plain he opposes.
The House speaker said conditions on higher taxes would include a revamped tax code to make it cleaner and fairer, fewer loopholes and lower rates for all, adding that "we're closer than we think to the critical mass needed legislatively to get tax reform done."
Boehner did not specify what loopholes House Republicans might consider trimming.
Obama spent a rare morning off Wednesday at his home on Chicago's South Side, then stopped at campaign headquarters to meet privately with staff to thank them for their work in the long, grueling campaign. Workers climbed on top of desks to get a good look at the president.
Obama and his family then flew back to Washington on Air Force One. The president appeared to be in a good mood, racing younger daughter Sasha up the steps, then calling out "Come on slowpokes" to wife Michelle and older daughter Malia.
Associated Press writers Julie Pace, Ken Thomas and Andrew Taylor contributed to this report.
- Farm owners fined for refusing to host a...
- Ice bucket challenge goes awry, firefighters...
- Bridezilla, meet 'Bridechilla'
- Obama announces new birth control fixes for...
- Deported Mexicans find new life at call centers
- Huckabee: 'Stop the fight' over Common Core
- Photographer is using portraits to combat...
- How poverty plays a role in Ferguson
- Farm owners fined for refusing to host... 119
- Obama vows justice for killers of U.S.... 29
- 'Don't know' if Missouri teen shot with... 26
- Police, protesters collide again in... 25
- Texas Gov. Perry assembles high-powered... 23
- Federal judge: Florida gay-marriage ban... 17
- Allow student loan bankruptcies,... 17
- Emerging solar plants scorch birds in... 15