JERUSALEM — For years, Prime Minister Benjamin Netanyahu of Israel, a conservative, has played a double act, competing domestically with his right-wing rivals in backing the settlement project all over the occupied West Bank while professing support for a two-state solution with the Palestinians.

Now, with the stinging United Nations Security Council resolution on Friday condemning Israeli settlement construction as lacking any legal validity, Israeli politicians and analysts on the right, on the left and in the political center say Mr. Netanyahu’s game may soon be up.

The Israeli right, feeling empowered by the advent of the Trump administration, which is expected to be more sympathetic to Israel’s current policies, is pushing Mr. Netanyahu to abandon the idea of a Palestinian state alongside Israel, long considered the only viable solution to the conflict.

Naftali Bennett, the leader of the pro-settlement Jewish Home party in Mr. Netanyahu’s governing coalition, with whom Mr. Netanyahu and his Likud Party compete for votes, is goading him to take on more extreme positions like annexing parts of the West Bank, adding to a sense in Israel that the real Mr. Netanyahu may have to stand up and decide which side he is on.