Theresa May is both the strongest and weakest prime minister of recent times.
Her strength lies in her current popularity, demonstrated by opinion polls and anecdotally. She is seen, rightly or wrongly, as the steady-as-she goes, sensible leader for the chaos of negotiating Brexit.
That strength extends to the attitude of the media. It was striking on the trip to the G20 in China with her and 20 or so UK journalists that the press is giving her the benefit of the doubt, in a way that it has not done since the early days of Blair.
Hacks' normal pursuit of snubs to a PM and gaffes by him or her seems to have been suspended.
For example, when Theresa May at various official functions was seated or positioned a long way from the Xis, Obamas and other great panjandrums, May was given the benefit of the doubt - seen as finding her feet, not deliberately marginalised as representing a country that has turned its back on maximising its international influence through membership of the EU, or as being punished by her Chinese hosts for questioning whether China's companies would be proper owners of British nuclear power.
So much for her strength - best seen as an extended honeymoon with the British people and the organs of the media.
Her weakness, however, is just as extreme - and also has two sources.
The Tory majority in parliament is wafer thin. And, lest we forget, her party is bitterly divided, still, over the EU - though now its split is about the structure of our future relationship with the EU, rather than whether we should be in the EU at all.
For Tories, the toxic question is what kind of trade off there should be between access to the single market for UK goods and services on the one hand and - on the other - the right or ability of EU citizens to continue to come here to live and work.
Oh, and there is also the electrifying issue of whether we should continue to pay anything to Brussels.
Against that backdrop, Mrs May's language on what Brexit means in a positive sense was conspicuously ambiguous.
For the avoidance of doubt, she has not formally ruled out either some kind of "voluntary" payments into the EU budget or preferential rights for EU citizens to live and work here - although she is under enormous pressure from the ultra sceptics in her party to do both.
So when it comes to formulating what Brexit actually means she is caught in the painful vice of what she and her advisers may see as necessary compromise on immigration and money for Brussels - that will deliver adequate access to the single market - versus what her MPs and members of her cabinet will actually tolerate.
It makes formulating a coherent plan for EU exit well nigh impossible.
And if she had any illusion that she has much time to pull off that impossible feat, it was shattered by Obama and Japan's Abe - both of whom delivered a stark message on behalf of the US and Japanese companies which have invested tens of billions of pounds in the UK, having been invited to do so by previous British governments on the promise of unfettered assess to the EU market.
Obama's and Abe's warning boiled down to this: their giant carmakers, drug companies, banks and so on would shift investment and jobs to the continent much sooner than Mrs May hopes and expects, unless they are given reasonable hope that there'll be no rupture of access to the single market and they'll have the ability to prepare in a careful and methodical way for whatever trading arrangements are in store.
This is serious - but it is extremely difficult to see what the prime minister can do to assure these long-term foreign providers of our prosperity that they shouldn't relocate at least some of their capital and knowhow across the Channel.
We'll start to see multinationals reduce their commitment to Britain within weeks. What impact that will have on the government's Brexit policy is hard to predict.
But surely there is a solution.
Mrs May could use her strength with the people and media to eliminate her weakness in parliament and party - by holding a snap election, since right now it looks as though she would win comfortably.
That is why some of her closest colleagues simply don't understand why she has categorically and unambiguously ruled out doing any such thing.
The explanation probably resides in the weakness she would be trying to eliminate: in the absence of a detailed prospectus for what Brexit actually means in practice, the Tory Party might well tear itself apart in an election campaign over what kind of withdrawal from the EU they were seeking.
Now it would be quite wrong to feel sorry for Theresa May, since she chose - as a Remain supporter - to be the prime minister who will deliver Brexit. But after her recent encounters with Abe and Obama she will certainly understand the gravity and magnitude of what she has taken on.