The real problem is not a political one, but one of car orientation. The Jerusalem Municipality and the State of Israel are very inconsistent in their transportation policies. They give lip service to promoting public transportation, but constantly build roads that will only encourage more private car use. The Municipality's claim that traffic congestion will be reduced by extending and widening the Begin Highway flies in the face of what planners and economists refer to as "induced demand" -- when you widen and extend roads you cause more people to drive, thereby ultimately increasing congestion. Instead of "easing" car-based access to central Jerusalem for residents of southern Jerusalem and Gush Etzion, it would be far wiser to improve access via public transit.
French tourist arrested for waving Israeli flag on Temple Mount (Haaretz)
from the article: New Jerusalem highway to cut Arab neighborhood in half