Barack Obama used his first public appearance since his return to the White House to issue a challenge to Republicans in Congress to work with him to prevent the economy going into freefall next year.

In a carefully posed statement from the East Room, during which he was accompanied by a crowd of "middle-class" Americans, Obama called on Congress to strike a deal before the January 1 deadline that would see an automatic rise in taxes across the board and swingeing cuts in spending.

"I am not wedded to every detail of my plan. I am open to compromise," Obama said. But, in a hint of the strife to come, he said that he still wanted to raise tax rises for the wealthiest American – a policy most Republicans in Congress vehemently oppose.

"We can't just cut our way to prosperity," the president said. "If we are serious about reducing the deficit, we have to combine spending cuts with revenue and that means asking the wealthiest Americans to pay a little more in taxes."

As part of the search for a compromise, the president invited to the White House for talks next week the most senior Republican leader left standing amid the election debris, House Speaker John Boehner, as well as other Republican and Democratic leaders in Congress.

As Obama grappled with the economy, his cabinet reshuffle and an agenda for the second term, Republicans were still trying to come to terms with the scale of the election defeat.

New details emerged revealing that his Republican opponent Mitt Romney had been confident of victory right up until the first voting figures came through on election night. A source inside his camp said that at planning meeting after planning meeting he had been assured of victory.

Not only had Romney planned an $25,000 fireworks display in Boston Harbour to mark his win but he had written only a victory speech, the reason his concession speech had been so brief. In a sign of how confident he had been, he had established a 200-strong transition team paving the way for the shift to the White House that even on election day was hiring more staff.

In his White House statement, Obama said that creation of jobs and economic growth was his top priority. There was an urgent need to deal with the impending fiscal crisis.

Without mentioning the word 'mandate", he waved his election win at the Republicans. He as not going to ask working-class Americana students and the elderly to pay for reducing the deficit while people like himself earning more than $250,000 were not asked to pay a dime more in taxes. "It was a central question during the election. It was debated over and over again, and on Tuesday night we found that the majority of Americans agree with my approach."

Only a few hours before Obama's statement, Boehner held his first press conference since the election. He suggested he was prepared to engage with Obama in a new spirit of bipartisanship both on working out a grand bargain on the fiscal cliff but also on immigration reform.

On the grand bargain, Boehner said: "This is an opportunity for the president to lead. This is his moment to engage the Congress and work for a solution that can pass both chambers … I am hopeful that productive conversations can begin soon."

But any bipartisan spirit might prove short-lived. He also also went on to say that, unlike Obama and the Democrats, he does not favour raising taxes on the wealthy and that removing some loopholes and cleaning up the tax code would be enough to do the trick. He also expressed opposition to raising taxes on the wealthy.

Part of Boehner's problem is that so far he has not been able to control all his colleagues, particularly those elected with Tea Party support.

Ominously, in his first answer to a reporter, Boehner was less than truthful, saying: "When the president and I have been able to come an agreement, there has been no problem in getting it passed in the House. "

Boehner and Obama reached an agreement on a 'grand bargain' to resolve the fiscal cliff crisis last year but when Boehner took it back to his colleagues in the House, they, led by the House majority leader Eric Cantor, blocked it.

Asked about the Republican post-mortem, Boehner was curt, restricting himself to saying just that conversations were under way.

After losing 434.36 points, or 3.28%, over the past two days, the Dow Jones Industrial Average held roughly steady following Obama's speech. Jack Ablin, the chief investment officer at BMO, said there were signs of compromise on both sides, and that hee expected a stop-gap compromise would be reached.

"I am still under the belief that they will a comprehensive compromise soon and hopefully a bigger deal next year," he said. "Hopefully I am not being naive."

Before the election 80 US business leaders, including Microsoft's Steve Ballmer and JP Morgan's Jamie Dimon, signed a letter calling for a balanced approach to tackling the budget deficit, including tax hikes and spending cuts.

On Friday United Continental airline boss Jeff Smisek told CNBC that the fiscal cliff could have a potentially more disastrous impact on his business than superstorm Sandy.

"It makes it difficult for us to operate," Smisek said. "The uncertainty that you get with the economy [and] a second recession would be bad for everybody," he said.