Barack Obama and the newly victorious Republican leadership in Congress have both pledged to seek common ground in a Washington riven by partisan division.
They will each, however, come to a lunch meeting at the White House on Friday with priorities that are anathema to the other side.
A weakened Mr Obama will be trying to rebuild the Democratic base that failed to vote for the party’s candidates on Tuesday, something he underlined with his commitment on Wednesday to bypass Congress on the issue of immigration.
Mitch McConnell, the incoming Republican Senate majority leader, has a different task – herding a larger and more conservative caucus behind measures that are tailored to corner Mr Obama, without overplaying the party’s hand.
Newly elected senators, such as Tom Cotton in Arkansas, Cory Gardner in Colorado and Joni Ernst in Iowa, were all backed by the party establishment as part of their effort to avoid the disaster of the 2010 and 2012 elections.
In those earlier polls, the Republicans were well positioned to take control of the Senate but were undone by out of the mainstream candidates in key races who could not command voter support.
“Superior Republican candidate quality is the single most decisive variable of the 2014 elections, especially when compared to candidate fields in 2010 and 2012,” said Jonathan Collegio, a former spokesman for the conservative campaign group, American Crossroads.
In policy terms, however, the new senators’ views may be more closely aligned to the most conservative wing on a range of issues, and the Tea Party champion in the chamber, Ted Cruz of Texas.
“The myth of the establishment taming the Tea Party is just that – a myth,” said Thomas Mann, of the Brookings Institution think-tank.
Ms Ernst has expressed support for the view that the UN is aiming to strip Americans of their property rights, called Mr Obama a “dictator” and expressed a willingness to take up arms “should [the federal government] decide my rights are no longer important”.
Mr Cotton, a favourite of the neoconservatives, wrote a letter while serving in Iraq attacking the New York Times for revealing a clandestine US intelligence programme and suggested that the paper’s reporters should be “behind bars”.
Mr Cotton and Mr Gardner served in the House of Representatives, entering the chamber in 2013 and 2011 respectively, at time when the Speaker, John Boehner, struggled to control a caucus that adopted positions far more conservative than he did.
Some of the Senate’s most conservative members will also rise to positions of power, with Jim Inhofe, of Oklahoma, likely to take over as head of its environment committee. Mr Inhofe is a climate change sceptic.
The Republican leadership under Mr McConnell has so far indicated their initial priorities will be firmly from the party’s policy mainstream.
The bills they will put forward from January, once the new Congress takes its place, include repealing a tax on medical devices and clearing the way to build the Keystone XL pipeline to transport crude oil from Canada. Both measures could win significant Democratic support.
“The priority is to put bills on the president’s desk that will move the country forward,” John Barrasso, a Wyoming senator who is part of the Republican leadership told the Financial Times. “It is going to be back to how Congress is supposed to work.”
Mr Barrasso also wants speedy action on easing curbs on liquefied natural gas exports – to undermine, he says, “Vladimir Putin’s energy dominance” – although in practice such a policy would takes years to come into effect.
But the Republicans will have to decide how far to push one of their core aims – repealing Mr Obama’s healthcare law, which is expected to be among their first votes in January.
Mr McConnell has made clear that he does not expect Mr Obama to sign such a bill, forcing the Republicans to move on to a second approach, of taking the legislation apart bit by bit.
Such a piecemeal approach may not be enough for the conservatives in the party. Mr Cruz continues to call for the “complete and total” repeal of the president’s healthcare legislation.
Any ability of Mr Obama and the Republicans to work together may have already been poisoned, by the president’s commitment to bypass Congress on immigration reform with an executive order.
Mr McConnell said this would be like a “red rag to a bull” for Republicans but for the moment, Mr Obama seems determined to wave it.
Mr Barrasso struck a more cautious note on Thursday about the impact of an immigration executive order, saying: “We will know a lot more after our discussions tomorrow what Mr Obama’s intentions will be.”
Additional reporting by Barney Jopson
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