Nic Robertson is CNN's international diplomatic editor. The opinions expressed in this article belong to the author.

(CNN) After a week in which world order has been wantonly thrown to the wind , it takes a strong character to venture into the eye of the storm.

Yet in the White House with the storm maker-in-chief is where British Prime Minister Theresa May will find herself Friday . If the speech that she delivered to Republicans on Thursday night is anything to go by, May believes she is the person to calm the weather.

In the five days prior to her meeting with President Donald Trump, decrees from his desk have signaled NAFTA's demise , effectively killed the Trans-Pacific Partnership , given the green light to walling America off from Mexico, and emboldened Israel to action that its neighbors fear.

He has also rattled China's cage -- not for the first time -- and caused global controversy over his comments concerning the use of torture.

That's a lot of diplomatic debris to have flying around.

She told her audience in Philadelphia that now was the time for the two countries "to join hands as we pick up that mantle of leadership once more, to renew our Special Relationship and to recommit ourselves to the responsibility of leadership in the modern world."

She also stated that while many of the institutions that Trump has previously been critical towards were "in need of reform and renewal to make them relevant to our needs today," he should "be proud of the role our two nations -- working in partnership -- played in bringing them into being, and in bringing peace and prosperity to billions of people."

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May arrives in a highly unusual position. She hopes in this visit not just to tame the weather but also to capitalize on Trump's need to calm these storms by securing a trade deal with the US.

Whether this is possible depends as much on Britain's economic needs as it does the President's willingness to be moderated by an ally.

Britain has recently created its own little whirlwind in Europe, known to storm chasers as Brexit. In May, Trump sees a fellow weather changer.

He's said that he's sure other EU member states will follow Britain through the exit.

The difficulty May faces in calming Trump and getting her trade deal is that she goes to Washington at a time of weakness for Britain.

Getting what she wants would be to accept a trade of symbolism for substance. He wants a fellow weather maker and respected world leader at his side; she wants the promise of a deal with the US to bolster her post-Brexit vision of a "Global Britain."

Britain's special relationship with America was ever thus. Churchill labored for years bringing the US to Britain's side. The war was sucking the life out of the UK, and Winnie knew only Uncle Sam could turn the tide. Only recently did Britain finish paying off that bill.

May's need is not as desperate as Churchill's, but the terms could be just as costly. And it's this calculation that could most influence how close she is willing to get to Trump.

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Based on his public comments both during the campaign and since the election, the PM certainly doesn't share his view of the world. Britain is committed to climate change and is concerned by Putin's lustrous longing for more territory. May values free trade, NATO, the EU and the hard-earned rights of women, as she made clear last night.

Then there's Trump's recently declared opinion that torture works. Even though House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell, both Republicans, have ruled out legalizing torture, the President's comments will have grated with May: Britain cannot cooperate with countries involved in torture.

What price, then, for such a relationship?

Trump's bold new world is already pushing the boundaries of tolerance. At the eye of the storm, May might find calm, but on the outside, the backlash has already begun.

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If she comes home clutching a piece of paper, she risks being saddled with more than a trade deal debt: she will be the first world leader to sign up to Trump's world order. That will be a hard image to shake. How, other world leaders will reasonably ask, can she square her "Global Britain" with Trump's protectionist policy of "America First"?

And the mud sticks: ask Tony Blair. The former Prime Minister paid a heavy price for his proximity to President George W. Bush. Already, in some corners, May is paired off with Trump: his "Maggie," as Thatcher was to Reagan. A strong woman who can talk European sense to his Manhattan damned-and-be-done style.

And while there is no doubt that May would like few things more than a good relationship with Britain's strongest traditional ally, it's worth thinking about what those few things might be.

To quote the Brexit campaigners, Britain left the EU to "take back control." Surely it wouldn't squander this apparent gain to be in hock to a man whose very idea of interlocution is leverage?

Some might ask who could be less appropriate an ally for "Global Britain" than a man whose idea of diplomacy is do as I say or hit the road, as Mexico's President found out the hard way earlier this week?

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Which brings us back to May's ability to talk some European sense to the President -- as Obama suggested she should -- and make him a less toxic trade partner.

Meeting with Trump and trying to bring him to heel is a seductive gamble. But it may be a price that an intelligent leader might ultimately decide to be a little steep.

May is right to look for allies in her quest to bring stability back to the world. Whether Trump is the right partner for her is another matter. It's a fine path to tread in her famed kitten heels.