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During the tough-fought Democratic presidential primary between then-senators Hillary Clinton and Barack Obama, at a wry moment during a televised debate, Clinton called Obama "very likeable" and he responded with the sterile retort, "you're likeable enough".

One can easily imagine David Cameron, the Queen, Prince William and the Duchess of Cambridge, Elton John and lots of British citizens waiting, on edge, for Mr Obama to offer the iconic words "special relationship", while knowing that no matter what the president utters, he really means the UK is just "special enough".

Mr Obama and his wife Michelle arrive for a state visit on Tuesday, and inevitably pundits will measure the trip's success along silly lines - on whether Mr Obama and Mr Cameron publicly call each other Barack and David, whether Mr Obama gets out on a cricket field, or better yet, whether they get sweaty playing basketball together.

But the truth about UK-US relations is that while there remains a unique and special character to the bond, it is not the "special relationship" it used to be.

America and Britain - or at least their leaders - have pretended unconditional love for the other for so long that the notion each would automatically support the other's adventures around the world seems itself the measure by which everyone tests every interaction, predicting a great collapse in mutual trust and support if both are not tightly hugging and caressing the other's objectives.

That is not a normal nation-to-nation relationship, and Mr Obama knows this.

Mr Obama has been incrementally de-emphasising the UK-US relationship as the place to start in the international community, not because Mr Obama doesn't like or appreciate the Brits but because the world is changing and he needs other key stakeholders to feel the love too.

When Gordon Brown was running Britain's show, Mr Brown had a habit of calling too much, of wanting lots of meetings and calls with Mr Obama.

During the UN General Assembly meeting at which Mr Obama chaired a Security Council meeting on nuclear non-proliferation, Mr Brown was hugely upset that Mr Obama wouldn't engage him more publicly.

Mr Brown wanted the world to see special relationship sizzle and Mr Obama would not oblige. Interestingly, the prime minister of another island nation ally, Japan's Yukio Hatoyama, also called a lot and was needy. Mr Obama, never liking to get too close to anyone, pulled away from both.

Mr Obama and Mr Cameron both know that managing the UK-US relationship requires neither under-doing the relationship nor over-doing it.

Pivoting off the killing of Osama Bin Laden in Pakistan, the UK is moving more aggressively toward withdrawing troops from Afghanistan without waiting for the US to give its blessing.

British defence budgets are under serious pressure, and this will inevitably erode the sense that the Americans and the British will ride into battle together wherever in the world the need calls.

Many areas remain in which the US and UK will be shoulder-to-shoulder hammering out problems - climate change, global financial stabilisation, and many national security and human rights arenas, Libya, for example.

But the British and the Americans are an increasingly anachronistic pairing: The by Mr Obama, Mr Cameron and French President Nicolas Sarkozy read like the last hurrah of the West engaged together for one last time on one last mission.

In the future, those national statements of purpose will need to include leaders of India, China, Brazil, Indonesia, South Africa, Turkey, among others.

And while all of these nations have important relationships with the US, the "specialness" of those relationships is growing while inevitably making the UK-US relationship relatively less special.

I have been asked a dozen times what gift Mr Obama might give the Queen or Mr Cameron, and I simply have no idea. Maybe a basketball for Mr Cameron and an iPad 2 for her Majesty.

But the best gift would be a coffee mug or t-shirt that said "US-UK: A New Normal."

The world is changing dramatically and a healthy US-UK partnership should be celebrated not by chirping about the extreme degree of specialness of the relationship but by what both do working together on emerging problems in the world - work that allows other nations to feel like they too get to sit at the special table.

Steve Clemons is founder and senior fellow of the American Strategy Program at the New America Foundation.