GAZA CITY (CNN) -

The Israeli Cabinet will meet early Tuesday to consider a cease-fire proposal that could provide a possible breakthrough in the ongoing crisis.

The proposal, put forward by Egypt, calls for all sides to cease hostilities in Gaza. It also calls for the opening of border crossings, once the security situation is stable, and for high-level talks among those involved.

Senior Israeli officials say the proposal is being taken very seriously; however, a Hamas spokesman described it as a "joke."

"We did not receive this declared paper from the Egyptians ... which means it's an initiative for the media. It's not a political initiative," said Osama Hamdan.

Speaking on CNN's "The Situation Room with Wolf Blitzer," he continued: "It's not really an initiative. It's not really an idea, what they are trying to do is to corner the Palestinians and to help the Israelis more."

Palestinian negotiator Saeb Erakat was more optimistic, saying he is hopeful that "we may see some real, real serious signs of a possible cease-fire in the next 12-24 hours."

"I know that some other leaders in Hamas have said we are not closing any doors for any initiative for a cease-fire," he said.

The stakes are high and climbing.

By Monday, the death toll from nearly a week of Israeli airstrikes on Gaza had reached 186 -- all of them Palestinians -- with at least 1,390 wounded, according to Palestinian health authorities.

The death toll is now greater than the number killed in Gaza during the 2012 war.

"We welcome Egypt's call for a ceasefire and hope this will lead to the restoration of calm as soon as possible," said U.S. State Department spokeswoman Jen Psaki, describing the situation as both dangerous and volatile.

'We have nothing'

Over the weekend, Israel dropped leaflets instructing residents to leave northern areas of Gaza, where it planned to carry out strikes. But Hamas, which controls Gaza, told people to stay put.

Ahmed, a resident of northern Gaza, loaded his family into a taxi Sunday to take them to somewhat safer ground in Gaza City.

"I don't answer to them," Ahmed said of Hamas' request. "I do what's best for us."

As they were getting into the car, explosions erupted nearby, prompting cries of fear from the terrified children.

It's the third time in the last five years that the family has had to flee their home.

Others stayed, because they felt they had no other choice.

"They will not vacate. ... Where do we go?" asked Ramez Al-Madhoun, who lives in a building with 20 people in the northern Gaza neighborhood of Beit Lahya. He said his building is home to seven adults, the rest children.

In Gaza City, where some streets are strewn with rubble, people are taking refuge in U.N. buildings. More than 1,000 gathered in one school alone.