SPEAKING at the White House after a stinging mid-term defeat, Barack Obama adopted a conciliatory tone. “Both parties,” he said, “are going to have to come together and compromise to get something done here.” Mitch McConnell, the Republican leader in the Senate, agreed, adding that he hoped the president would work with Republicans on spending, energy and trade agreements. “The question,” said Senator McConnell, “is how do we meet in the middle?” That was in November 2010. There followed a government shutdown, two flirtations with a sovereign default over the raising of the legal limit on government borrowing, and the least productive Congress since anyone began counting.

The president and Mr McConnell once again made similar pronouncements about working together after another disastrous mid-term election for the Democrats on November 4th. Those who believe that this time will be different argue that divided government works better when Congress is wholly controlled by one party and the presidency by the other. When the House and the Senate are in the hands of different parties, according to this line of thinking, it is too easy for one to blame the other for intransigence and avoid governing.

Before this idea is tested by the new Congress in January, there is a lame-duck session to finish. These sessions of Congress are typically productive when compared with the healthy-duck sort. Because the budget process pushes controversial decisions towards the end of the year, a disproportionate number of important votes on spending will fall in a session where 12 senators (or 13, if Mary Landrieu loses a run-off in Louisiana on December 6th) will not have to face the voters again and can therefore smooth their passage. In 2010 the expiring Senate allowed gay people to serve openly in the military, ratified a treaty on nuclear missiles with Russia and extended some tax cuts.

Funding the government past December 11th, the deadline to avoid another shutdown, should be straightforward. The confirmation of the 35 ambassadors and 16 judicial nominees currently before the Senate will be harder. In 2008 Democrats held a series of pretend sessions to prevent George W. Bush from making appointments while the chamber was in recess. Republicans may now try a similar wheeze; the Senate cannot go into recess without the agreement of the Republican-controlled House. Such shifty manoeuvres are now all too common.

Congress may give the president fast-track authority to negotiate foreign-trade deals. And there are other areas where Mr Obama and Republican leaders agree. Both sides want to lower America’s high taxes on companies, which contribute to the parking of just over $2 trillion of profits overseas. Agreement may not lead anywhere: a sensible corporate-tax reform would lower rates and close loopholes; if done properly, it would mean a tax increase for those firms that now benefit from exemptions. Since most Republican members of the House have signed a pledge to voters never to raise taxes, this will be a hard sell. A more straightforward, though less important, change is likely when the new Senate takes up the Hire More Heroes bill, which the House has already passed and will revive in January. This would allow companies to hire veterans whose health care is covered by the Department of Veterans Affairs, without them counting towards the overall headcount for the purposes of the Affordable Care Act. Under that law, all firms with 50 or more full-time staff must provide them with health cover. The way this bill works with Obamacare suggests that House Republicans know the law itself is not going away. (A bill to repeal it may find its way to the president’s desk, but he would veto it.) A second likely tweak will be to repeal Obamacare’s 2.3% tax on medical devices, which will slightly increase the deficit but not affect the way the health law works. Republicans will also try to change the definition of full-time work, which triggers an employer’s obligation to provide insurance, from 30 hours a week to something lengthier. Mr McConnell may attach things that the president would rather avoid to proposals with broad support. Approval of the Keystone XL pipeline, which would carry crude oil from Canada’s tar sands to refineries on the Gulf coast, fits this description. But no compromise seems likely over global warming. The president wants to do something about it, as his tentative deal with China this week shows (see article). Most Republicans do not; Mr McConnell campaigned partly on rescuing his state’s coal mines from federal bullying.

Where are the new faces?

The new Senate will have to vet the president’s appointments. The most pressing of these is a new attorney-general. The president has nominated Loretta Lynch, a federal prosecutor, to take over from Eric Holder. Ms Lynch, who has a Harvard law degree, is well qualified for the job. She also has a remarkable family story: her great-great-grandfather, a free black, fell in love with a slave and, unable to buy her freedom, became enslaved again so he could marry her. Ms Lynch’s grandfather, a pastor, helped blacks escape from the organised racism of Jim Crow states. These qualifications should see her confirmed, but her nomination hearing is likely to get caught up in a fight over immigration. The president has repeated a threat to use his executive power to slow the deportation of illegal immigrants—though he has yet to reveal how exactly he will do this. Senators Ted Cruz of Texas and Mike Lee of Utah have promised to press his nominee on whether such a move would be legal.

After his party’s drubbing in the mid-terms, Mr Obama might be expected to reshuffle his team. Yet he shows no sign of doing so. Several cabinet members are newish and unlikely to be turfed out yet. Since Rahm Emanuel left in 2010, no chief of staff has lasted much more than a year. The president will be in no rush to get rid of the current one, Denis McDonough. One adviser whose importance is likely to grow is John Podesta, who was Bill Clinton’s chief of staff when Republicans controlled Congress in the 1990s. He helped the two sides work together productively, despite the impeachment battle.

Many in Washington were hoping that Valerie Jarrett, Mr Obama’s closest confidant, might move. Her vast influence, vague job description and lack of policy expertise infuriate Democrats and Republicans alike; but she will probably stay put. The president trusts her, and the mid-terms have made his job lonelier than ever.