At Harvard University on Saturday the penny finally seemed to drop. After a cliche-ridden chronicle of China's achievements, from the invention of gunpowder to the victory of Mao's revolution, Mr Jiang said he would take questions.
The professors, sensitive to charges that they had packed the audience with China-sympathisers, did their best. With shouts of protesters from outside the hall audible, they picked two questions from the hundred they said they had received. The first asked about the army's assault on Tiananmen Square eight years ago, the second about Tibet, the third - taken, apparently at Mr Jiang's impromptu instigation, from the floor - about his understanding of American-style democracy.
But it was the first that signalled the change. True, the Chinese leader spent most of his answer defending his own efforts - as mayor of Shanghai and national leader - to find out about people's concerns and he did not mention Tiananmen Square. But then he said: "It goes without saying ... we may have shortcomings and even make some mistakes ... However, we have been working on a constant basis to further improve our work."
There, for the first time, in answer to a question about Tiananmen, was an admission of error. The connection was not direct but it was there to be made - perhaps the first time the word "mistake" had crossed a Chinese leader's lips in that context.
It was said US officials had tried time and again to convince Mr Jiang to express at least regret for the Tiananmen events. At his press conference with President Bill Clinton on Wednesday there had been only justification. The "correct conclusions" had been drawn: the government had to act to preserve stability and unity in a country of 1.2 billion people.
This led him into disagreement with Mr Clinton, who condemned China as being "on the wrong side of history" on political dissent. Next day Mr Jiang seemed to soften a little, when he talked to Asia specialists about the need to improve democracy and the rule of law in China.
Mr Jiang's tour was seen by many China-watchers as comparable with Deng Xiaoping's epic visit in 1979, when his smiles and spontaneity won many hearts. Mr Jiang left an impression of efficiency, some potentially valuable trade deals, but little warmth.
But there is just a chance, that, with his impressions of US hi-tech and the New York Stock Exchange, Mr Jiang may also have taken back some of his hosts' questions about China. If so, Americans may in time come to regard his trip more charitably as time well spent.