If Hamas is kept out of the peace process, analysts say, they will do all they can to scuttle it before it begins. But if they are allowed in, they will probably block any chance of success.
Similarly, if they are kept out, it is difficult to see how the moderates will be able to deliver. But if they are allowed in, there probably won't be anything to deliver, the analysts say.
So far the government is determined to keep Hamas out, which is having a significant effect on the ground. Shut out by Israel, the ostracized Hamas leaders are growing increasingly desperate, Ben Caspit, political analyst for the Ma'ariv daily, said.
"Hamas leaders know that if Palestinian President Mahmoud Abbas comes back from the summit with a major achievement, it will create an existential problem for them," Caspit wrote. "As time goes by, efforts to carry out a major terror attack to torpedo the process will intensify. One Qassam in the 'right' place at the 'right' time could prevent us from going to Washington in November, and push us with much sound and fury into Gaza in October."
The official Israeli policy is to keep Hamas isolated on the assumption that the split in Palestinian ranks serves the peace process -- the thinking is it frees the moderates to cut a deal. Once that happens, the Israelis hope the radicals' power will wane.
This explains the government's tough line on Gaza.
Three weeks ago it declared Gaza an "enemy entity," with all that implies in regard to civil sanctions, such as withholding electricity and fuel. Moreover, the Israeli army has since stepped up its pressure on militant groups in a concerted effort to prevent a major terrorist strike that could jeopardize the planned November summit.
In an address to the United Nations General Assembly on Monday, Foreign Minister Tzipi Livni ratcheted up the political pressure, calling for heightened international isolation of Hamas and the adoption of a treaty that would bar terrorist organizations like Hamas from taking part in elections.
Critics of the government line argue that Hamas won an election, is supported by nearly half the Palestinian people and cannot be ignored. They suggest taking seriously the latest Hamas calls for a cease-fire.
But the government seems bent on breaking Hamas' power. Over the past several days, the Israel Defense Forces has carried out undercover operations and pinpoint strikes to prevent attacks. Last week, an undercover unit pre-empted a suicide bombing by capturing a number of known Hamas terrorists in the West Bank. The fingered terrorists led them to a hideout in south Tel Aviv where a suicide belt was found ready for a would-be bomber.
Rocket attacks from Gaza were also forestalled. Israeli air, tank and infantry units killed approximately 20 Palestinian terrorists in targeted assassinations and military operations against launch teams.
All this is just a prelude for a major ground operation in Gaza, according to Defense Minister Ehud Barak. The idea would be to deliver a crippling blow to Hamas and significantly reduce Qassam rocket fire from Gaza aimed at nearby Israeli towns and villages.
One idea is to hold on to security zones inside Gaza to push the rockets out of range. The military operation would be launched after the November summit, but a "successful" terrorist attack could change the timing.
Under pressure, Hamas leader Ismail Haniyeh has been calling for a cease-fire. Barak argues that Hamas would exploit any respite to build up its forces. He believes the IDF has the terorists on the defensive -- and he wants to keep it that way.
Some experts maintain that the government is making a huge blunder and that it should accept a cease-fire as a first step toward bringing Hamas into the peacemaking orbit. Former Mossad chief Ephraim Halevy argues that Israel could get a long-term cease-fire -- 10 to 20 years -- which could pave the way for accommodation with all the Palestinian factions.
Yohanan Tzoreff, an expert on Palestinian society and government at the Herzliya Interdisciplinary Center, says that without bringing in Hamas, Israel will not be able to reach any significant deal with the Palestinians. He proposes that when Israel releases Palestinian prisoners, as it did this week, it should include Hamas, too.
"This might even help Abbas convince Hamas to join in agreements which so far they have not been prepared to accept," Tzoreff said in an interview.
The government also has its critics on long-term solutions for Gaza. Its plan is for a Gaza-West Bank union joined by an overland highway and governed by a moderate leadership. But Yair Naveh, a former head of Central Command, says that a Gaza already impoverished and overcrowded is heading for a population explosion and even greater poverty.
In that situation, he says, the last thing West Bankers want is a land connection allowing young Gazans to come into the West Bank in great numbers, taking jobs and women, and foisting religious values on a largely secular population.
Therefore, Naveh proposes separating Gaza and the West Bank, and Israel handing over to Gaza relatively large tracts of land from the Negev to give it the land reserves it needs to handle its growing population. According to the Naveh plan, Israel would take an equal amount of land from the West Bank by annexing large Jewish population centers.
So where does Hamas stand? It is saying many different things. Some spokesmen reject the political process, others defy the Israeli military and threaten to send suicide bombers back onto Israeli streets.
But Haniyeh has adopted a relatively conciliatory tone, urging Hamas and rival terror groups to stop firing Qassam rockets at Israel as part of a bid to achieve a cease-fire. Moreover, his chief political adviser Ahmed Yousef has been trying to portray Hamas as part of the moderate camp."Hamas is a bulwark in the face of radical and militant ideas and trends," Yousef declared. "The West should ask itself whether it wants the moderation and realism of Hamas or the dogmatism of radical groups that subscribe to the clash of civilizations theory."
The question for Israeli decision makers: Is the Haniyeh-Yousef line worth exploring, or would the very attempt prove a trap? So far the Israeli government's answer has been a resounding "no" to any dialogue with Hamas.
Leslie Susser is the diplomatic correspondent of the Jerusalem Report.