The key question is whether Netanyahu will commit to the two-state solution and the creation of a Palestinian state. So far, he has refused to do so, and his hawkish foreign minister Avigdor Lieberman, warns that Israel is no longer in the business of making concessions for peace. The early signs suggest a confrontation with the United States.
Netanyahu has said he will continue the peace process, but by not supporting Palestinian statehood, he is breaking with the policy of previous Israeli governments. Instead of a state, he has talked of a degree of self-rule with the development of the Palestinian economy as an urgent priority.
The U.S. administration has not shied away from making its position clear. Mitchell underlined the U.S. commitment to the two-state solution during talks in Algeria Tuesday, echoing President Obama's very clear commitment during his recent speech in Turkey.
"We believe that the two-state solution, two states living side by side in peace, is the best and only way to resolve this conflict, and we will be pursuing that objective in meetings," said Mitchell.
Netanyahu heads a right-wing coalition of political parties aligned with the settlement movement and those who believe Israel must retain control of the West Bank. He is seen as pragmatic, but it is not clear how much room for maneuver his partners will allow him.
The strategic priority in his relationship with the United States is the Iranian nuclear threat and his concerns about Obama's desire to talk with Tehran.
Palestinian Negotiator: Mitchell Means Business
At his office in the West Bank city of Jericho, veteran Palestinian negotiator Saeb Erekat told ABC News he believes Mitchell means business and has the backing to push the Israelis toward meaningful negotiations.
"Sen. Mitchell told us one thing. He told us I'm not here for the process. I'm here for peacemaking, and if he stays the course we're going to be in good shape," said Erekat.
But he also sounded a warning to the United States in response to new Israeli plans to build new settlements and to demolish dozens of Palestinian homes in East Jerusalem.
"I think for us this is the real test for the U.S. administration. If Israel builds more settlements and demolishes homes in East Jerusalem, we don't even need to meet each other, that's it! We will be as Palestinian moderates, no longer relevant to our people. We've told the Americans this."
Despite the concerns, the traditional diplomatic courtesies are continuing. Palestinian Authority President Mahmoud Abbas called Netanyahu this week with holiday greetings for the Jewish Passover. Officials from Netanyahu's office said the tone of the conversation was friendly.
But Abbas' public statements have hardened in recent days, saying he will not engage in peace talks unless Netanyahu agrees first to the two-state solution and halts settlement construction.
It has all been a bit like diplomatic shadow boxing so far, but this week Mitchell will want to find out exactly where Israel's negotiating red lines are to be drawn.
When he flies on to Cairo Friday night, he should know the scale of the task at hand, and whether the new Israeli government will be a willing partner for peace.