By Jonathan Beale
BBC News, Washington
How is Barack Obama going to make it up to Gordon Brown?
Mr Obama and Mr Brown share common political ground
Is he bringing a better gift for the Prime Minister this time - like DVDs he can actually watch?
What about a proper news conference, rather than the "camera spray" that was given to Mr Brown when he visited the White House?
Even in Washington, there is a perception that President Obama did not exactly roll out the red carpet when Mr Brown visited last month.
Reginald Dale of the Centre for Strategic and International Studies, a foreign policy think tank, says it showed that Barack Obama may not have an "instinctive feel" for America's relationship with Britain and a wider Europe.
He says the body language of the Obama-Brown meeting was all wrong and could be hard to correct.
If Mr Obama does come to Britain bearing more gifts for the Browns, then it is only an admission that the last ones were inadequate.
G20 LONDON SUMMIT
World leaders will meet later this week in London to discuss measures to tackle the downturn. See
our in-depth guide
to the G20 summit.
The G20 countries are Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, Mexico, Russia, Saudi Arabia, South Africa, South Korea, Turkey, the United Kingdom, the US and the EU.
Of course, the present that Gordon Brown really wants from Mr Obama is his full support for his G20 agenda.
The earlier slight may be more manufactured than real.
It is worth remembering that Mr Brown was the first European leader to visit the Obama White House.
Mr Obama and Mr Brown share a similar Keynesian strategy for economic recovery - though the UK Prime Minister can only look on with envy at the power and popularity of America's Commander-in-Chief.
Despite Barack Obama's rock star status across the continent, his economic policies are still viewed with suspicion
On the face of it, President Obama is in tune with Europe as a whole.
There is broad agreement on issues like climate change, Middle East peace and Iran.
As Mr Brown put it in his speech to Congress on 4 March, Europe's leaders are now more pro-American than ever.
But only up to a point.
Despite President Obama's rock star status across the continent, his economic policies are still viewed with suspicion as yet another example of bloated American excess.
Germany's Angela Merkel has made it clear she will not be signing up to a massive global stimulus package.
The (former) Czech Prime Minister put it more bluntly, describing the Obama economic strategy as a "road to hell".
Europe's public may love Obama, but some of Europe's leaders are unwilling to take lessons from the country they blame for creating this crises.
The reality of the G20 is that Mr Brown's lofty ambitions will not be met.
No one else is talking about "a global new deal".
But it will be much easier to paper over the cracks between Mr Obama and Mr Brown than to conceal the gulf that exists within Europe itself.
European leaders will be keen to be photographed with Mr Obama
The Brown-Obama relationship may lack a certain chemistry, but there is at least some common ground.
That might be less true of the President's relationship with other European nations.
Nile Gardner, a British Eurosceptic who works for Washington's centre-right Heritage Foundation, has described the Obama White House as the "first wholeheartedly pro-European federalist administration".
This is, perhaps, a bit of an exaggeration - but it is true that Mr Obama's focus has been on trying to rebuild ties with Europe - particularly with Germany and France, the countries Donald Rumsfeld once dismissed as "old Europe".
But now, in the first real test of this fresh start, Europe is unable to deliver for Mr Obama.
Germany is saying "Nein" to a global stimulus.
When Barack Obama goes to Strasbourg for the Nato summit, Germany will also be saying "nein" to his request for more troops in Afghanistan.
When Mr Obama goes to Turkey and expresses his support for their membership of the European Union, he may well have time to ponder once again why Germany is so opposed.
I am only using Germany to prove the point that Europe does not speak with one voice.
When the President visits Prague (the Czech Republic holds the rotating EU presidency) it may feel more like winter than spring.
The Czech government, which backed President Bush's missile defence shield, has been left hanging in the wind - a bargaining chip as the White House ponders its relations with Russia.
Europe and indeed the world's leaders may not see eye to eye with the Obama administration on a range of issues.
That is not to say that they do not want to be seen with this President.
They will all be queuing up for their photo opportunity, hoping that some of the Obama magic will rub off.
Gordon Brown may have reason to smile more than most - he does have more in common with the new President than most.
But he and every other world leader at the G20 will be eclipsed by another.
It may be the only time on this trip that America recognises a star as bright as their own.
It is the image that will be plastered all over the US TV networks: when Her Majesty the Queen meets Barack Obama.
Who said the special relationship did not matter?