Forget the two-state solution: start thinking about the four-state problem. The phrase comes from Palestinian negotiator and analyst Ahmad Khalidi, who has toiled for decades to see two states side by side, one for Palestinians, the other for Israelis. Now, though, he sees one strong state, Israel, surrounded by three statelets. The first is the West Bank, ruled by the secular nationalists of Fatah. The second is Gaza, for nearly two years the fiefdom of Islamist Hamas. The third is the surprise: still in embryo, we got a glimpse of its future earlier this month.

Militant Jewish settlers in Hebron resisted their eviction from a disputed house by not only hurling stones and debris at Palestinians nearby - and daubing black stars of David on Muslim gravestones in what Israel's prime minister Ehud Olmert called a "pogrom" - but also by turning their fire on the soldiers of the Israel Defence Forces. These images were a shock to the Israeli system, confirmation that a hard core of Jewish settlers now exists that has next to no loyalty to the state of Israel, and that indeed regards the state as godless and illegitimate - and which is prepared to raise its hand to the teenage men and women who comprise the bulk of Israel's conscript army. Soon we might speak of Israel, the West Bank, Gaza and a new, zealous, rebel entity: call it Judea.

We are not quite at that point yet. But add it to the long list of developments causing veterans of the Middle East peace process - a saga so long-running that it's the Mousetrap of international negotiations - to lose faith in the two-state solution, even as that model enjoys near global support among the world's governments, restated again yesterday, whether at the United Nations security council or at Olmert's meeting in London with Gordon Brown.

The causes for despair are numerous, starting with that fragmentation cited by Khalidi. Palestinians who once believed the split between Fatah and Hamas was transient and reparable now worry the division is hardening, that there is no figure on the horizon capable of putting this sundered people back together. They ask why Hamas would come back under the authority of Palestinian president Mahmoud Abbas. What would be in it for them?

And yet so long as the Palestinians remain divided, Abbas is too weak to do a meaningful deal with Israel, one that would bind all Palestinians. Indeed, conversations with those on both sides in the last week have told a remarkably similar story: neither Israelis nor Palestinians believe they are capable of reaching an agreement.

The mood is hardly conducive. A month-long blockade of Gaza, with Palestinians there denied access to fuel, medical equipment and much else, may not have garnered a great deal of attention here but the rising human cost, of sick patients and darkened schools, is a staple of the nightly news on television around the Arab world. The anger is directed mostly at Israel, for enforcing the sanctions, imposed in response to the discovery of secret tunnels into Israel from Gaza. But Egypt is blamed too, for failing to open its border, thereby bringing respite to those in desperate need - as are the European Union and the US, both of which are party to the embargo of Hamas. On Friday, Hamas's six month-long ceasefire, which has mainly held, will expire. Few would bet on it being extended.

Meanwhile, Abbas faces an expiration date of his own: his presidential term runs out on 9 January. He is hinting that he will step aside, allowing elections for a new leader. Even those unimpressed by Abbas - by his remoteness, his inability to act as a unifying, national figure - see his departure as an invitation for more division and paralysis.

The stalemate has roots on the other side, too. Olmert's time is also running out; Israel will have new elections on 10 February. Polls predict a return to power for Binyamin Netanyahu and Likud, whose defining trait is a nationalistic scepticism about the peace process. Even if that were to be overcome, Israel has its own inbuilt divisions, expressed in coalitions perennially too fragmented to make the concessions that have to be made.

Besides, there are plenty in Israel's policy establishment who think the status quo is bearable, that Palestinians pose nothing like the existential threat of, say, a nuclear Iran. They're happy enough to have a process but are not really serious about peace. As I heard one senior Israeli official put it recently: "Negotiations are good, results are bad."

Some respond to this bleak landscape by focusing on individual elements within it and imagining how they might be improved. Maybe new Palestinian elections would produce a useful outcome. After all, the latest survey from pollster Khalil Shikaki has Fatah leading Hamas by 42% to 28% - with Fatah polling especially strongly on Hamas's turf in Gaza. Or perhaps Netanyahu will follow the Nixon-to-China principle and, as a man of the right, do the deal. After all, when he last served as PM a decade ago, he proved to be more pragmatic than his reputation had suggested. Or there will be a miracle and the new, dovish party founded by former Camp David negotiator Gilead Sher, and backed by literary giants Amos Oz and David Grossman, will sweep to unexpected victory.

Dream on. Rather than hoping the factors thwarting a two-state solution might change, it is surely more rational to step back and rethink the entire approach. Britain's foreign secretary, David Miliband, is fond of quoting Eisenhower's maxim that, when faced with an intractable problem, the first move is to make it bigger. Frustrated by the impossibility of making peace between two peoples, why not up the ante and seek to make peace between Israel and the entire region? A comprehensive peace or, as Miliband put it in a speech last month, "a 23-state solution - 22 members of the Arab League plus Israel".

This is not as fanciful as it might seem. The Arab peace initiative of 2002, which offered full normalisation of relations in return for Israel's withdrawal to its 1967 borders, is still on the table. Indeed the Arab League wrote to Barack Obama just last week, urging him to work for Middle East peace, with their initiative as the basis.

There are problems with the Arab plan. For one thing, there has been no public diplomacy for it, no public face for it - no equivalent of Anwar Sadat's breakthrough visit to Israel, proving the sincerity of his desire for peace. And how would it work in practice? Khalidi wonders how on earth 22 Arab countries are meant to reach "simultaneous orgasm", coming to an agreement with Israel all at the same time.

And yet the logic behind it is compelling. Right now, the Palestinians don't have enough to offer Israel to make the sacrifices required for a peace deal worthwhile. But an accord with the entire Arab world, that would be a prize worth bending for. And, while today's Palestinian leadership is too weak to make compromises on, for instance, Jerusalem, united Arab support would give the Palestinians all the cover they need.

Fear of Iran might motivate the Arabs to come together. A falling oil price could concentrate the mind too. And as always, the sine qua non is the active intervention of the US. Some Israeli officials believe that, after the Bush era, the US is no longer capable of imposing its will on the Middle East. Starting next month, President Obama will have a chance to prove them wrong - and solve one of the world's most persistent problems into the bargain.

freedland@theguardian.com