After a day spent in Egypt waiting for Yasser Arafat, the Palestinian leader, and Ehud Barak, the Israeli Prime Minister, to sign a revised version of the Wye Agreement, a testy Ms Albright was looking increasingly like the best man at a wedding where the bride and groom have not turned up.
She flew to Israel and spent three hours yesterday morning locked in talks with Mr Barak. "Both sides are playing the Americans for their own ends," said one observer. "The Palestinians want the Americans to mediate because they are so much weaker than the Israelis. Arafat has had some success here."
The focus of Ms Albright's visit to the Middle East was originally meant to be the so-called Syrian track. Ms Albright intended to go to Syria tomorrow to edge the government towards starting negotiations with Israel. But in the days before her trip started it was the Palestinian issue that once again came to the fore.
Mr Barak appears to have got his way over releasing no more than 350 Palestinian prisoners. But he has paid a diplomatic price. The relief felt in Washington when he defeated Benjamin Netanyahu in the Israeli election is subsiding. American officials are beginning to wonder how different Mr Barak is from his predecessor.
Yoel Marcus, a commentator in the daily Haaretz, says Mr Barak's "adoption of a Don Corleone tone in making an offer you can't refuse damaged the process of working towards mutual goodwill". He adds that when the Israeli- Palestinian diplomatic process "turns into a haggling match in a Persian bazaar, the Palestinians have the upper hand over us".
Here Mr Barak may be committing the same mistake as Mr Netanyahu. Mr Arafat has few cards compared with Israel. He rules a collection of isolated cantons. He has no military option. The 2.5 million Palestinians on the West Bank and in Gaza - their freedom of movement controlled by Israel - are more impoverished than they were at the start of the Oslo peace process in 1993.
But Mr Arafat's agreement is necessary for any deal to be concluded. By refusing to release a final 44 Palestinian prisoners, Mr Barak forced Ms Albright on Thursday to exude forced optimism with increasing desperation before rushing to Jerusalem to see the Israeli leader. If Mr Barak had shown more flexibility, he would be in a much stronger position in future to reduce the US role.
Even with an agreement on the implementation of the Wye accords, American involvement is not likely to diminish. In theory, Mr Barak's position is that he wants to separate Israelis and Palestinians. But in reality, the handover of 40 per cent of the West Bank to Mr Arafat's full or partial control merely complicates the mosaic of competing authorities on this small piece of land. Fine highways linking Jewish settlements curl between Palestinian villages, creating continuing friction.
Under the version of the Wye Agreement, known as Wye 2, now being implemented this friction will not subside. The Palestinians get more land, but no settlements are removed. There will be two safe-passage routes between the West Bank and Gaza but real freedom of movement will depend on the stringency of Israeli security measures.
Ms Albright will now try to focus on the Syrian part of her trip. Syria warmly welcomed Mr Barak's election and heavily publicised its instructions to small and moribund guerrilla groups based in Damascus to desist from armed attacks on Israel. Activity by Hizbollah, the Islamic resistance to Israel in Lebanon, was curtailed.
In theory, a deal between Syria and Israel should be easier than one between the Palestinians and Israel. A treaty could be signed whereby Israel withdraws from the Golan Heights and southern Lebanon in exchange for demilitarisation and a full peace treaty. The Palestinians, by contrast, with half their seven million people refugees, are unlikely to be satisfied by any treaty, however final it is intended to be.
The Syrians have tactical reasons for expressing their willingness to negotiate with Israel: they want to get off the US list of states supporting terrorism. But they have said little to indicate that they really believe Israel is willing to leave Lebanon and the Golan. As time passes in Israel the gloss on Mr Barak's election victory will also diminish and his highly fragmented coalition government will be more difficult to hold together. This will reduce his ability to show flexibility in negotiations with Damascus.
Not that there has been much sign of Israeli flexibility in the talks with the Palestinians over Wye 2. Negotiations start next year on a framework for negotiating the final status of Palestinians. But Haim Ramon, an Israeli cabinet minister, said last week that he saw no chance of an agreement on Jerusalem or Palestinian refugees, two of the most important issues.
Ms Albright can claim to have successfully brokered the agreement between Mr Arafat and Mr Barak that she will witness over the next 24 hours. But the great labour it has taken to produce Wye 2 - itself the renegotiation of a renegotiation - shows that her portly form will be back in the Middle East before long.