The most remarkable interlude during last Friday's Hamas rally in Gaza City came when the central political arguments between it and Fatah were set to music. Two members of a highly professional vocal group, one representing each faction, sang a good-humoured but topical duet in which the central complaints about the international boycott of the Hamas-led PA were aired with surprising candour. "Can't you recognise Israel just a little bit?" intoned the "Fatah" man. "We are not getting salaries. You are making us beggars."
That this diverting musical number should be performed at a time when armed men from both Fatah and Hamas were already firing at each other in the streets seemed incongruous. But no more so, perhaps, than when Mahmoud Abbas, the Palestinian president, announced his intention the next day of revisiting the Palestinian public's election of Hamas last January.
That Mr Abbas should choose to try to solve an increasingly bloody conflict by calling for fresh elections less than a year after the last ones, something which Hamas, the faction actually in government, has said it will not accept, hardly seemed like a recipe for harmony.
The Palestinian president is in a weak position, but he is not a fool. The gamble was the product of his frustration at the failure of negotiations with Hamas on the kind of "national unity" government that might have lifted the crippling international economic siege, in theory of the Palestinian Authority, but in practice of the Palestinian people.
And he will have known that it would attract at least some international support. Indeed, Tony Blair seemed impatient at yesterday's press conference in Ramallah that other countries were not giving more support, financial as well as moral, to Mr Abbas after his "landmark" speech on Saturday as speedily and publicly as he had.
But this is where the problems begin. Mr Blair presumably realises that if Britain - and perhaps the US - were exposed as the strongest backers of Mr Abbas and his plan, it would not help the standing of either. And this is not only a function of Iraq. Mr Blair is almost certainly sincere about wanting to see solutions in the Israel-Palestine conflict and in believing, with justice, that the benign effect of this would extend well beyond the immediate region. He has told at least one Israeli minister that he would like some - as yet unspecified - role in Middle East peacemaking after he leaves office.
There are signs of an effort to engage friendly Arab neighbours as interlocutors on behalf of the Palestinians. But in much of the Arab world, as at home, his credibility has hardly been improved by his stance in the Lebanon war. It is easy to see why he would want others to back Mr Abbas as vigorously as he does.
But Mr Abbas's strategy is not an easy sell. Mr Blair made the valid point yesterday that Mr Abbas also has a democratic mandate as president and a duty to use it in times of crisis. But this will not stop Hamas exploiting an already wide perception on the streets of Gaza and the West Bank that the Western world is in favour of democracy in the Middle East until it gets a result it doesn't like.
But there are other questions about the plan. Supposing Hamas finally decided not to boycott such elections; it isn't clear that Fatah would win. Most polls give Fatah a slight edge. But Khalil Shikaki, the most respected Palestinian pollster, has already predicted that the result would be "desperately close". Even the political boomerang of all boomerangs - a Hamas presidency and legislature - "cannot be ruled out".
But supposing Fatah do win. Are Hamas just going to accept their lot? Part - though only part - of the history of the past few increasingly bloody weeks has been the refusal of elements in Fatah to accept the result last January. Why would Hamas be any different, especially after an election it never wanted? Why would it not act to undermine a new government pledged to negotiating a two-state solution, not least by resuming attacks on Israel as well as on a Fatah government?
An alternative scenario canvassed by some British officials is that the threat of elections might just persuade Hamas finally to agree a "national unity" government of non-affiliated academics, which would lift the blockade. Certainly there are signs that Britain has been somewhat keener on such an outcome than the US. But Ismail Haniyeh told Friday's rally that the donations he attracted in Iran, Syria and Qatar had "lifted the siege". This looks like a Hamas less interested in a national unity deal than a month or so ago, when Mr Haniyeh offered to resign as prime minister.
Diplomats present the idea, obliquely floated by Mr Blair yesterday, of beefing up Mr Abbas's security forces as a "deterrent". But it's hard to escape the conclusion that the US at least would not be averse from Mr Abbas embarking on a bloody civil war against Hamas, which it persists in seeing as - like Hizbollah - merely an extension of Iranian-backed extremism. Yet even if this analysis were not at best a dangerous oversimplification, why would Mr Abbas succeed where Israel has failed in six years of conflict by wiping Hamas out?
There are, of course, many might-have-beens. It will be long debated whether it would not have been better to impose on Hamas less stringent conditions than prior recognition of Israel and renunciation of all future armed operations - such as a demand that it merely halted all actual violence. Mr Blair knows very well that these are harder conditions than the UK demanded in the Northern Ireland peace process. Without so harsh a blockade, Hamas would have been tested in office without being able to use the blockade as an excuse for failure, let alone being driven to greater dependence on Iran.
What is not a matter for debate, now that efforts are being made once again to bolster Mr Abbas, is that far more could have been done to help him when he first became president in 2005. If Israel had been anything like as generous with prisoner releases as Mr Abbas pleaded with it to be - and as Mr Blair was in the Northern Ireland context - Mr Abbas would be in a far stronger position now.
In Mr Blair's defence, any international engagement here is welcome. And Mr Abbas is a decent man, whose frustration is increased, by all accounts, by a belief that Mr Olmert may be genuinely interested in talking now his policy of unilateral withdrawals from the West Bank has vanished along with hopes of an outright victory in the Lebanon.
The hope must be that somehow the dangerously deepening Palestinian crisis can be overcome. The fear is that the efforts to which Mr Blair committed himself yesterday will be too little, too late.