The PLO Executive Committee supported seeking statehood recognition at the UN in September. President Abbas is not backing away from the idea (so far, anyway).
The US is likely to veto any resolution at the UN Security Council. At best, the PA may hope for a supportive resolution in the UN General Assembly. If so, I hope the resolution writers listen to this op-ed, as I noted the other day.
But assuming the resolution is the current PA line, I have a hard time seeing that the passage of a UN resolution would bring the PA closer to Palestinian statehood. It would not change the occupation on the ground. If it increased international pressure on Israel (which it very well might not), many members of the current Israeli government and Israeli public would simply see that as further proof of irrational, international hatred for Israel. Thus, it would serve as further evidence that Israel needs to protect itself without reliance on others (except, for some, the US), without risky treaties with Palestinians or other Arabs, and without major territorial withdrawals.
I certainly am open to hearing about scenarios where UN action does somehow change the status quo.