I don't think it will change much to be honest. Just buys him time. This is the same cycle, just with higher initial Israeli death and hostage count. But ultimately this too shall pass. For everyone. Right now Israelis getting all of the sympathy. Once house to house fighting and aerial bombing slows down, it will be the Palestinians turn and we're going to see retrospectives etc on their plight and people w/ no real connection to the region declaring how we finally need to come to a resolution. People in the US will be like "uhh this is too much, I got my own shyt I'm dealing with" and start focusing on the election or trump. Israeli govt will be a mess, no one can bring a coalition, more settlements will be built etc etc etc.
Rinse and repeat.
You know what's crazy? In a few months the narrative is going to flip and Israel will be seen as somewhat of a pariah state.
Right now we're in the fog of war.
Bibi is very unpopular in his own country. A lot of what we're seeing right now is the benefit of any doubt that's typically given in short term to allies who have been attacked.
The weeks after 9/11, nobody would've said anything if the US went on a rampage bombing anything that moved. It's the same with this situation.
But once major operations have ended and the full scale of what's happened is seen. All the children/women etc...the media narrative will start to shift. Europeans, left or right, who are generally less pro Israel will start putting more pressure on their governments.
All the while Hamas will continue to exist, not just bc their foot soldiers will have melted back into the population but also bc their leaders are living openly in Qatar and other places.
Negotiations are being pushed as a stalling tactic, by both sides not just Hamas. Israelis want to see how much Qatar can squeeze from Hamas, and to get a better understanding of Hamas' will/determination to fight. They also want to use this as "proof" to the US/international community of their willingness to stop fighting, assuming certain objectives are met. But there's little to no chance they will accept Hamas' conditions (no drone coverage over Gaza), or maybe they will delay a short while to allow the US to move in assets that will allow them to take over.
Right now the main sticking point is how far Israel is willing to go for the hostages. Hamas primary hostage strategy/objective is to exchange them for all of most of the Palestinians currently in Israeli jails. If they do that, I think they basically guarantee their survival going forward. In the past the Israelis went to great lengths to get back hostages. In 2011 they freed more than 1000, including murderers/terrorists, just for 1 Israeli soldier, the difference being that there was a lot of political pressure to make that deal. There was even a group of Israeli mothers whose children were victims of terrorist attacks planned/committed by Palestinians that Hamas were demanding be released, that supported the exchange. A lot of ppl have said in retrospect that was a mistake and my guess is that netanyahu don't see this moment as one where they need to be so generous (both from military/security or political standpoint).
Netanyahu is also smart enough to realize that biden doesn't want this as a distraction during the election. My guess is that he thinks from Bidens perspective the best outcome is for Israel to quickly subdue Gaza and then the US can parachute in with a very generous proposal of support (political solution/economic aid etc) for the Palestinians. Israel probably realizes that what Biden doesn't want/can't afford is for this war to go on block by block, week by week, pausing for one week at a time for "negotiations", only to restart, then pausing again while 5 hostages are released. I don't know how many young voters would be sufficiently turned off by what they're seeing to abandon Biden or stay home, but any amount is too many for Biden and the Dems.