Al-Ghad's sources said that some of the names on Israel's list include hostages that Hamas considers to be soldiers, whereas Hamas says it will only release the sick, the elderly, and children.
Family members called for a deal but also attacked Prime Minister Benjamin Netanyahu and his family for launching a 'hate' campaign against them.
Knesset member Michal Woldiger expressed an opinion contrary to much of Israel's senior leadership - that she would support ending the war for the hostages's safe return.
Current progress in the talks remains stuck for the time being, as the two sides remain at an impasse over a couple of Israeli demands.
The rule of silence does not apply to the families of the hostages, who need to speak out to keep the issue on the agenda and ensure it remains a top priority.
Netanyahu is anxious to avoid starting off on the wrong foot with the grievance-obsessed president-elect, who recently told Time magazine that he doesn't really trump the prime minister.
“Matan, your mother is here, and so are we until you return," protester signs read.
One issue that remained unsolved is that Hamas has yet to formulate a list of hostages it is willing to release from captivity in Gaza.
Bipartisan press conference calls for swift hostage release amid emotional family pleas.
Michael Levy recounted the last time he heard his brother's voice and gave a heartfelt plea to the United Nations Security Council.
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