Exactly what Nicolas Sarkozy meant by describing Benjamin Netanyahu as a "liar" is not immediately clear, and the French President is unlikely to prolong the episode by explaining it. But it is safe to assume that Mr Sarkozy has become increasingly unconvinced of Mr Netanyahu's sincerity in saying he is willing to negotiate a two-state solution with the Palestinians. By insisting the Palestinians recognise Israel as a "Jewish state" and by resuming a surge in Jewish settlement building, Mr Netanyahu has given no sign that he envisages the minimum deal the Palestinians could accept.

The source of Mr Obama's frustration is similar, but compounded by two other factors. One is the part played by Israel – and especially Mr Netanyahu, a long-term friend of the Republican right – in US politics, which Mr Obama clearly judges makes it impossible to apply the pressure he would like on the Israeli leader. And the other may be a sense of ingratitude. Mr Obama has secured virtually nothing in return for his generosity, from opposing the Palestinian bid for UN recognition to a repeated delivery of weaponry and security co-operation. The candour of the presidential exchange may be surprising; the content much less so.