By Paul Reynolds BBC News Online world affairs correspondent

To understand how strong the basic relationship between George W Bush and Tony Blair is, it is worth going back to the scene at the White House on the evening of 20 September last year.

President Bush was about to make a speech to Congress which would be his chance to stamp his authority on a crisis in which he had wobbled - his first comment had been to refer to the suicide bombers as "folks".

It could be useful for Blair to state his differences over Arafat

Tony Blair arrived from New York, a bit late because of heavy traffic.

But Mr Bush was calm and, while officials from both sides made conversation, he took Mr Blair aside to a window overlooking the south lawn and for 20 minutes they talked.

One of the officials there was the British ambassador, Sir Christopher Meyer, a former Downing Street spokesman. He said later that Tony Blair's support for George Bush that evening was "absolutely instinctive."

The prime minister then went up to Congress, getting a special mention and round of applause as the president rose to the occasion with the best speech of his life and declared his war on terrorism.

Caricature

That kind of "instinctive" rapport has carried Tony Blair through many a policy disagreement with the Bush administration - through Bush's rejection of Kyoto, the imposition of American tariffs on steel and increased American subsides for agriculture.

Mr Blair also kept quiet during international rows over Mr Bush's anti-missile plans.

His silence was rewarded when Russia itself accepted the proposals and the issue went away.

Has the moment come for Tony Blair to side more openly with those European leaders who do not have the same instinctive sympathy for the American president?

He rejected the cartoon view of Mr Bush as the ignorant Texas gunslinger, having been impressed with the president at their first meeting in early 2001 at Camp David.

He accepted that George Bush has an American focus - all leaders have their national and political interests at heart - and that Mr Bush is determined not to suffer the fate of his father who was seen as being too favourable to foreigners.

Right not might

Mr Blair has loyally thrown his troops onto the battlefield in Afghanistan because he, too, believed that the fight there was a fight for right, not might.

Above all, he has understood the total dominance of American politics of the attacks of 11 September.

These events have cast their shadow over the Middle East as well.

One reason Mr Bush has turned against Yasser Arafat is that the Israelis gave him evidence that the Palestinian leader had financed suicide attacks on Israel.

In Mr Bush's view, this was terrorism.

Disagreement too far?

Now there is another disagreement, over the future of Mr Arafat.

Is it a disagreement too far?

Has the moment come for Tony Blair to side more openly with those European leaders who do not have the same instinctive sympathy for the American president?

Mr Blair knows that a potentially even greater crisis lies ahead which might require that he draws on the credit he has built up with Mr Bush

The track record indicates that Mr Blair will seek to smooth over the problems.

He does not need and does not want a row with Mr Bush over the Middle East.

But at the same time, it is quite useful for Tony Blair to state some difference.

It might do him some good among restless Labour MPs at home who regard him as too close to a divisive president.

Crisis to come

It recalls Harold Wilson's quiet refusal to send British troops to Vietnam when Lyndon Johnson was president.

That refusal did not cause a major rift but it signalled a useful difference.

The same might be true in this case.

And Mr Blair also knows that a potentially even greater crisis lies ahead which might require that he draws on the credit he has built up with Mr Bush - an American military attack on Saddam Hussein.

If that happens, Mr Blair will want a voice at the table - or at the window overlooking the south lawn.