If the Palestinians wanted to stop this new construction, they could agree to begin negotiating for a state ASAP. Both Israelis and Palestinians could agree on benchmarks toward agreement while the building is stopped. They could make negotiating away the settlements a priority in the negotiations. It seems like whining and stomping their feet in public is PA's preferred to actually doing anything for themselves to stop the Israeli building. It seems like maintaining this feeling of victimhood and powerlessness is preferred by the Palestinian Arabs.
Let's keep in mind that it is Abbas not Netanyahu, who has refused face to face negotiations, for several decades. Even with all the efforts from Kerry Abbas walk away from negotiations, despite the fact that Netanyahu he accepted all the Palestinian preconditions, including halting of all settlement construction, and waited for Abbas to come to the table for nearly a year, Abbas still refused to negotiate.