Some strategists say Israel should use the opportunity to force Gaza to look outward to Egypt, its natural Arab hinterland, and thereby reduce and eventually end Israeli responsibility for Gaza's fate. Others say such a handover of responsibility would expose Israel to worse terrorism than ever and that Israel instead should clamp down on all crossing points: between Israel and Gaza, Gaza and Egypt, and Israel and Egypt.
Still others are focused on the threat the tricky new situation poses to Israel's ties with Egypt and its peacemaking efforts with Palestinian moderates.
Guy Bechor of the Herzliya Interdisciplinary Center said that the border breach has created conditions for a total Israeli disengagement that would leave Egypt responsible for Gaza, as it was before the 1967 Six-Day War.
"For the first time since 1967, Egypt has been sucked into Gaza, and worse, Gaza has been sucked into Egypt," he said.
Bechor maintains that Israel's erstwhile policy of policing Gaza along the Philadelphi route, which separates Gaza and Egypt, was short-sighted and ultimately self-defeating. More than protect Israel, it protected Egypt from Gaza's Palestinian terrorists.
The fall of the wall, he says, has reopened the possibility of close working ties between Hamas and Egypt's Muslim Brotherhood, which could threaten the Egyptian regime.
Therefore, Bechor said, if left alone to deal with Gaza, Egypt will keep a much tighter rein on Hamas than Israel ever could. Israel just has to sit back and do nothing and the situation will take care of itself, he avers.
Former Israeli national security adviser Giora Eiland also believes the new situation provides an excellent opportunity for Israel to rid itself of responsibility for Gaza.
To cement the break, he proposes detaching Gaza from the customs union with Israel and the West Bank.
As part of the Oslo agreements, Gaza, the West Bank and Israel form a single customs entity: All goods coming into Gaza or the West Bank are subject to Israeli-level duties to keep prices in the three areas more or less equal. Moreover, all three use the Israeli shekel as legal tender.
Eiland's proposal would cut off Gaza economically from Israel and the West Bank and force it to turn to Egypt for sustenance and trade.
With the breach of the border, Eiland said, Israel also could cut off all fuel and other supplies to Gaza and insist they instead come from Egypt. He says the huge Gazan shopping spree on Egyptian soil in the wake of the wall's collapse demonstrates that Egypt can provide a realistic economic alternative.
Eiland acknowledges that an open border with Egypt will accelerate the flow of heavy weaponry into Gaza, but said Israel should deal with that by defining Gaza as an "enemy entity" and establishing a deterrent balance with it -- the way it does with enemy states like Syria.
Furthermore, pushing Gaza into Egypt's hands would sever the connection between Gaza and the West Bank and weaken the Palestinian national movement -- a development that Eiland believes would serve Israeli interests: Instead of looking to Israel or the West Bank, Gaza would look to its Arab neighbor.
Although this might not facilitate a formal peace deal between Israel and the Palestinians, it would certainly make the conflict more manageable, Eiland said.
For other analysts, however, the idea of an open border between Egypt and Gaza is a strategic nightmare.
Maj.-Gen. (res.) Yom Tov Samya, a former head of Israel's Southern Command, which is responsible for Gaza and the Egyptian front, says Israel must act quickly to reinforce its control along the border with Egypt "from the Mediterranean to Eilat."
This means increasing patrols along the entire Israeli-Egyptian border and reasserting Israeli control over the Philadelphi route, which Israeli forces handed over to the Egyptians shortly after Israel's withdrawal from Gaza in 2005.
If these steps are not taken, Samya said, terrorists will be able to move out of Gaza into the Sinai and threaten Israeli civilian populations across the weakly defended Israeli-Egyptian border -- to say nothing of the free flow of heavy weapons from Egypt into Gaza. Rather than opening Gaza to Egypt, as Bechor and Eiland suggest, Samya urges sealing it off tighter from Egypt.
"The holes in the Philadelphi route could lead to regional war," he warns.
The Likud Party's Yuval Steinitz, a former chairman of the Knesset's Foreign Affairs and Defense Committee, takes a similar view. Steinitz added that if the border between Gaza and Egypt is left open, Egypt is likely to become a strategic ally of Hamas -- helping it the way Iran does today -- and that this could reopen the possibility of conflict between Israel and Egypt.
"Only effective Israeli and American pressure is likely to block this dangerous trend," he maintained.
The Israeli daily Ha'aretz recently took this line of thought further. In an editorial titled "Double threat to peace," the newspaper argued that the fall of the border constitutes a danger to Israel's strategic peace with Egypt and threatens to undermine peacemaking with the Palestinians. It emphasized the serious threat of terrorism from the Sinai and said Israel could be pushed into a risky ground operation in Gaza in an effort to stabilize the situation.
Ha'aretz called for an urgent Israeli-Egyptian summit before the situation deteriorates.
Israel's government has yet to adopt any of the new policy suggestions. Prime Minister Ehud Olmert seems to be toying with the idea of detachment from Gaza, while Defense Minister Ehud Barak would like to see stronger action by Egypt to seal its border with Gaza.
In the meantime, following a court order, Israel has renewed the supply of fuel and cooking gas to the strip.After meeting with Olmert on Sunday, Palestinian negotiators said the prime minister told them that he wants to transfer responsibility for Gaza's humanitarian problems to Egypt. He also said he was opposed to the Palestinian Authority controlling Gaza's border crossing points because that would entail a deal between the Fatah-led Palestinian Authority and Hamas.
Olmert also apparently warned the negotiators that if they tried to exploit the current situation to negotiate a power-sharing arrangement with Hamas, Israel immediately would suspend the post-Annapolis peace talks.
Barak, generally thought to be behind the failed Gaza siege policy -- bringing economic pressure to bear on Palestinians in Gaza in the hope that it would lead them to topple Hamas -- is now urging Egypt to reseal the border with Gaza.
"It's in its interest as much as Israel's," Barak said.