UNDER the pressure of Israeli sanctions, Gaza this week blew a gasket. On January 23rd Palestinian militants blasted holes in the metal wall along the sealed Gaza-Egypt border. A bulldozer broadened the gaps. Tens or even hundreds of thousands of Palestinians poured through to buy fuel, food, spare parts and other supplies. Egypt's president, Hosni Mubarak, was annoyed but ordered his troops to let them in, saying they were “starving due to an Israeli siege”. On the Palestinian side, armed men from Hamas, the militant Islamic group that controls Gaza, checked the returning shoppers for contraband and weapons.

The shortages in Gaza have grown gradually worse since Israel, having declared Gaza a “hostile entity”, began restricting imports three months ago in response to a continued rain of Qassam rockets onto nearby Israeli towns. Despite repeated warnings from Israeli human-rights groups that diesel for the strip's only power station was running out, Israel closed the border crossings altogether on January 17th, after a rise in the numbers of Qassams. Three days later the power plant, which supplies around 30% of Gaza's winter-time electricity needs—the rest coming from Israel and Egypt—shut down, leaving large parts of the strip without light, heat or running water.

Israel at first accused Hamas of exacerbating the crisis for political ends, though foreign aid-workers in the territory say Hamas does not interfere with the power station. Israel restored supplies the next day, but said it would keep them to the bare minimum needed to prevent a shutdown. Officials saved face by claiming that Gaza had “got the message”: and, indeed, the Qassam fire did diminish sharply.

Hamas, which an Israeli newspaper reported had planned the border breach months in advance with another militant group, will probably co-operate to reseal the border. It cannot afford to anger Egypt, its only mediator with the West.

But the squeeze on Gaza has led to what Israel wanted to avoid: co-operation between Hamas and its rival party, Fatah. Though Fatah still hates Hamas for ousting it from Gaza in June, the interim Palestinian Authority government in the West Bank appointed by Mahmoud Abbas, the Palestinian president and head of Fatah, has become increasingly anxious to end the blockade. It proposes putting non-partisan forces in charge of the Gaza border crossings, to overcome Israel's refusal to open its side of the crossings so long as the other side is controlled by Hamas. Hamas leaders this week supported the idea, and foreign countries including America, Israel's strongest ally, seem keen too. Such a change, Israel fears, could relieve the pressure on Hamas.

Not that the pressure was working well anyway. Polls show that Hamas's support, which fell after its showdown with Fatah, has stabilised. The Qassams, which rarely kill but keep over 20,000 Israelis living near Gaza in permanent fear, continue to fall. Israel's collective punishment of the 1.4m Gazans, and its missile attacks on militants that often kill some civilians too (65 Gazans died in the first three weeks of January), merely draw ever louder condemnation at home and abroad.

Yet Ehud Olmert, Israel's prime minister, must feel he has no option. Doing nothing is politically impossible. Negotiating a ceasefire, which Hamas has offered—although there are doubts about whether it can impose one on the other militant groups in Gaza that fire the rockets—would undermine his campaign to unseat Hamas since it was elected two years ago. And a massive army operation to take control of the strip, which some hawks advocate, would mean many deaths on both sides, and could leave the army policing Gaza indefinitely, a resounding failure for Israel's “disengagement” in 2005.

Sanctions on Gaza may not work, but they look tough to the Israeli public, and Mr Olmert needs to look tough. Next week a final report on the 2006 Lebanon war is expected once more to be highly critical of his performance, and political rivals are sniffing blood.

Yet the current policy is self-defeating too. Israel is holding peace talks with Mr Abbas in the hope that Gaza's citizens, seeing real promise of a Palestinian state, will rise up and, if not overthrow Hamas—which says the peace process is worthless—at least make it more conciliatory. But the more Gaza suffers, the harder it is for Mr Abbas to continue those talks. And if a Qassam hits a busy Israeli school playground, Israel's politicians may feel obliged to hit back so hard that they destroy the peace process for good. Israeli and Western policy has been to try to ignore Gaza, but Gaza is showing ever more clearly that it cannot be ignored.