Tony Blair has long claimed one of the greatest benefits of his close friendship with George W Bush was his ability to exert influence over the only remaining superpower.
By Nick Assinder
Political Correspondent, BBC News website
The prime minister's former spin doctor Alastair Campbell repeated that message regularly during interviews before and after the election result.
Blair needs to show influence
Now that a strengthened Mr Bush is back in the White House, that claim is going to be put to the test, with Labour backbenchers wanting to see concrete examples of that influence at work.
Until now, the most quoted example was the fact that the prime minister persuaded the president to seek further UN resolutions before attacking Iraq.
But some Labour MPs claim the move was purely cosmetic as Mr Blair had already assured the president he would support war on Saddam whatever the UN decided.
Apart from that contested example, the prime minister's critics claim it is hard to point to other areas where British influence has swung the president away from a particular course of action.
Trade disputes, the Middle East roadmap, and the Kyoto Protocol on climate change are all examples of where the president has refused to budge.
Now, it is being suggested in some Labour circles, it is payback time.
Straw ruled out war on Iran
Tony Blair will press the president to make significant moves on all these areas - with the Middle East peace process top of his agenda.
Speaking in the moments after the official result was announced, Mr Blair declared: "I have long argued that the need to revitalise the Middle East peace process is the single most pressing political challenge in our world today.
"Therefore, we must be relentless in our war against terrorism and in resolving the conditions and causes on which the terrorists prey".
Tough on terrorism, tough on the causes of terrorism as it has been characterised.
At the same time, Foreign Secretary Jack Straw has fired a shot across the president's bows over any move towards future military action against other nations such as Iran.
Such action would be "inconceivable" he said, certain in the knowledge it would also almost certainly be inconceivable for Mr Blair to support any such action in the wake of the Iraq crisis.
"I don't see any circumstances in which military action would be justified against Iran," Mr Straw said.
Bush has not been persuaded in the past
Meanwhile, Environment Secretary Margaret Beckett has claimed domestic and world opinion would ultimately persuade the president to move on global warming.
She fell short of suggesting the US would sign up to Kyoto, but claimed pressure "from the bottom up" would lead to action to combat climate change.
Over-arching all this is the prime minister's continuing desire to offer a bridge between the US and Europe - an ambition which was thwarted by the war.
These are big demands and, at the moment, it is impossible to accurately predict how the second-term president will proceed.
One forum in which they will be tried is the G8 meeting of global leaders which the prime minister will chair next summer.
If Mr Blair is to lift the sense of depression, even fear, that now hangs over the Labour backbenches in the wake of the US result, he must bring home the bacon.