The roots of the current carnage in Gaza and Israel lie squarely in the "new Middle East" - not the democratic wave that has swept the region over the past two years, but the policy adopted by the Bush administration in 2006, to unite authoritarian Arab regimes with Israel and the US to exorcise Hizbollah, Hamas and Iran.
That year, the US secretary of state, Condoleezza Rice, told Lebanon's prime minister, Fouad Siniora, that bombs falling on Beirut were "the birth pangs of a new Middle East". But just as the US had failed to impose its will in Iraq, Israel failed to destroy Hizbollah in its 2006 invasion of Lebanon, or to break the grip of Hamas during its three-week pummelling of Gaza in the winter of 2008.
The new Middle East that began to emerge in early 2011 is very different to the one Ms Rice had in mind. US-allied dictators have been swept away, and the emerging Arab democracies are no more interested in following Iran than they are in fighting it. Washington's regional influence has actually declined.
Which brings us to the question of Gaza: President Barack Obama was sworn into office in January 2009, just days after Israel had completed its "Operation Cast Lead", which left 1,300 Palestinians dead. But even at the height of his ultimately doomed effort to restart the Israeli-Palestinian peace process, Mr Obama essentially maintained his predecessor's policy on Gaza.
Mr Bush and Ms Rice had sought to reverse the results of the 2006 Palestinian elections, won by Hamas, but the Islamists pre-empted a US-backed coup attempt in 2007, brutally driving Fatah's security forces out of Gaza. Unable to restore Gaza to the control of its Palestinian allies, Washington instead joined with Israel in enforcing an economic siege aimed at toppling Hamas. The US hoped the immiseration of Gaza, combined with boosting aid to President Mahmoud Abbas in the West Bank, would marginalise the Islamists.
Hamas's rocket fire into Israel in late 2008 was an explicit effort to force the Israelis to lift the blockade; instead it brought Cast Lead, and a new ceasefire that simply froze an untenable status quo. Having seen the devastation Israel was capable of unleashing, Hamas over the next four years largely kept the peace despite the blockade - strengthening its authoritarian rule over Gaza, and policing more militant rivals, including emerging Salafist radicals.
The likes of Turkey and Qatar saw the dangerous dysfunction in the US-Israeli strategy to isolate Hamas, and sought instead to encourage a more pragmatic orientation from Hamas through engagement. Qatar recently pledged half a billion dollars of investment to rehabilitate Gaza, but at the same time urged Hamas to refrain from violence. Hamas appeared caught between pragmatism and pressure to maintain its resistance posture through allowing, and sometimes joining, a measure of renewed rocket fire. But it was reportedly discussing a renewed truce when Israel's "Operation Pillar of Defence" began last Wednesday.
Many Israeli commentators saw the operation as reinforcing Benjamin Netanyahu's election narrative of himself as the best custodian of Israel's national security. But Mr Netanyahu is a preternaturally cautious leader. His domestic political interests require a short demonstration of steely resolve, but also avoiding a repeat of Cast Lead, which resulted in unprecedented international isolation for Israel. By limiting the operation's goal to the vague benchmark of "restoring Israel's deterrence", Mr Netanyahu has allowed himself to declare victory whenever he chooses.
The problem is that Hamas has a vote on when the war ends, too, and while the fact that missiles from Gaza reached Tel Aviv and the environs of Jerusalem could be used by the Islamists to claim a demonstration of "deterrence" of their own, those same developments could also prompt further escalation from the Israelis.
But a long war, particularly one that brings Israel's commercial capital under fire, could start to look like a reckless gamble. Mr Netanyahu needs a ceasefire that he can proclaim a victory. Hamas does, too.
Hamas is also in the grip of a politburo election, at a moment of choice between the more pragmatic path encouraged by Qatar, Turkey and the Muslim Brotherhood in Egypt, and heeding the pressures from more militant groups on the ground in Gaza to maintain a resistance posture or lose ground to the Salafists.
Brokering a truce will fall, once again, to Egypt. But this is not the same Egypt that served as the wall against Hamas's back while it took a beating from Israel in 2008. President Hosni Mubarak saw Hamas as an enemy; the Muslim Brotherhood recognises Hamas as part of its ideological family. And today's government in Cairo is far more responsive to Egyptian public opinion.
On Friday, President Mohammed Morsi sent his prime minister, Hisham Qandil, on a solidarity visit to Gaza, and also, it was widely assumed, to promote a ceasefire. The fact that the Israelis announced they would suspend operations during the visit suggested back-channel coordination. But if Egypt and Turkey can deliver Hamas consent for a ceasefire, the US would have to do the same with the Israelis.
But the new Egyptian government is unlikely to simply restore calm under a blockade. Mr Morsi told the UN in September that justice for the Palestinians was the basis on which Arabs would judge the West. Hamas might cease firing, but it won't surrender. Nor will Egypt and the other regional players expect Hamas to simply accept Israel's writ; it may require opening the border crossing with Egypt.
Simply restoring the calm of February 2009 is untenable; a Gaza under siege doesn't remain stable for very long. Even Israel is effectively negotiating with Hamas, expecting it to keep the peace. But such deals will continue to unravel unless they open the way to broader progress for Gaza, and a change in how the West and Israel deals with its leadership.
Condi Rice is long gone. It's long past time for the US to retire her Gaza policy, too.
Tony Karon is a New York-based analyst
On Twitter: @TonyKaron