The next 24 hours will be critical in terms of the prisoner exchange deal with Israel, senior Hamas sources told Arab media on Wednesday morning. The organization's leaders, who left Cairo on Tuesday evening, are meeting in the offices of Hamas' political bureau in Damascus to decide whether to accept Jerusalem's latest offer.

According to one of the sources, who spoke to London-based Arabic-language al-Hayat newspaper, the organization's leaders – including those who arrived from Gaza - are at odds over the issue. Some believe Hamas should insist on releasing every single prisoner on the list handed over to Israel, while others hold a more pragmatic approach and understand that not everything can be achieved in the negotiations.

According to another newspaper, al-Sharq al-Awsat, the deal is being delayed over four names of arch-terrorists, led by Ibrahim Hamed, who was arrested in 2006 for his involvement in deadly terror attacks. Israel, according to some of the reports, is only willing to release him if he is deported outside the Palestinian territories.

The three other prisoners delaying the deal, according to the report, are Abdullah Barghouti, Abbas al-Seid, and Ahmed Saadat.

One of Hamas' senior members, Dr. Khalil Al-Hayya, said Tuesday night that his movement continued to hold on to its demands in terms of the deal securing the release of kidnapped soldier Gilad Shalit. He warned that Israeli stubbornness in the face of Hamas' stipulations could torpedo the swap.

"It appears that internal Israeli problems are having a negative influence, but we are waiting for the coming hours to see if there will be a deal by the weekend," said another source.

Noam Shalit goes to rabbi

Meanwhile, Israel is waiting for Hamas' response and attempting to lower expectations. Prime Minister Benjamin Netanyahu promised Tuesday that if and when a deal is finalized, it would be brought to the government's approval "and to a public discourse."

Ministers are expected to convene Wednesday for a pre-scheduled diplomatic-security cabinet meeting, where they may learn more about the deal's outline and timetable.

The Shalit family members are continuing their battle to have their son released. Gilad's father, Noam, is expected to meet Wednesday with Ministers Yuval Steinitz (Likud) and Uzi Landau (Yisrael Beiteinu) in an attempt to change their minds and have them vote in favor of a possible deal. He will later try to gain the support of Israel's chief rabbis as well.

The Palestinian prisoners' families are also exerting heavy pressures in a bid to find out whether their sons are included on the list of inmates slated to be released. It is still unclear whether former Fatah Secretary-General in the West Bank Marwan Barghouti, who is serving several life terms for murder, will be freed as part of the deal.

The wife of Ahmed Saadat, the secretary-general of the Popular Front for the Liberation of Palestine who is jailed in Israel for planning the murder of Minister Rehavam Ze'evi, says she has not received any information from an official source that her husband is expected to be released in exchange for Shalit.

"My husband prefers the deal to include veteran prisoners and those sentenced for longer jail terms than him. In addition, he would like to see sick prisoners, women and minors released before him," Abla Saadat said.