Warily. Neither side thinks the other is in any position to make a real deal, and it’s not exactly clear how the US government could change their mind.
Palestinian President Mahmoud Abbas doesn’t trust the Israeli government, which is currently led by a right-wing coalition. Settlement expansion is one of the main reasons; settlement construction reached a seven-year high under Israeli Prime Minister Benjamin Netanyahu’s leadership. Abbas sees the rapid expansion during Netanyahu’s time in office as strong evidence that Israel is attempting to make a Palestinian state impossible. While Netanyahu did freeze settlement expansion everywhere but Jerusalem for 10 months starting in November 2009, Palestinians wanted a total freeze, and so only sat down to talk in the ninth month (the talks went nowhere).
Netanyahu has been a critic of a two-state solution to the conflict for decades, and while he’s expressed support for one now in theory, many believe his commitment isn’t genuine. He’s the first leader of Likud, Israel’s major right-wing party, to endorse a two-state solution while in power, which he did under heavy American pressure in 2009.
But while campaigning during the 2015 Israeli election, which his party won fairly resoundingly, Netanyahu announced that there would be no Palestinian state under his watch. It’s a statement he’s tried to walk back, but one that’s consistent with his long-held belief that Palestinians can’t be trusted to be peaceful neighbors.
Israel has real reasons to be skeptical of the Palestinian side. One major one is the Hamas-Fatah split. Since Hamas took control of Gaza, Israel has been concerned that any peace agreement with the Palestinian Authority wouldn’t stick in Gaza, where it has no real control. That’s especially worrying for the Israeli leadership given Hamas’s public commitment to Israel’s destruction. Moreover, it’s not clear that Abbas could sell Palestinians on the concessions he’d inevitably need to make in order to make a deal with Israel.
The two sides’ basic skepticism of each other’s willingness and ability to make peace is the fundamental reason that the peace push led by US Secretary of State John Kerry fell apart in April 2014. Since then, the Palestinians have turned toward a pressure campaign designed to isolate Israel internationally and put pressure on the Israeli leadership to make peace, which has had little success.