The Palestinians cannot get membership in the UN because the United States would use its veto.  But they have other options.  A month ago they were voted in by a wide margin to the United Nations Educational, Scientific and Cultural Organization, UNESCO.  This compelled the United States to cease funding to UNESCO because of an American law that prohibits contributing to any organization that recognizes the Palestinian Liberation Organization which the US considers to be a terrorist arm.

The US has no veto power to prevent entry to UNESCO or 14 other special UN agencies.  Quoting Gwynne Dyer:

If the Palestinians apply for membership in each of these organisations over the next year or so, they will probably get the same 88 percent majority when it comes to a vote on membership. None of the countries that defied the United States and voted Palestine into UNESCO is going to humiliate itself by changing its vote at other UN agencies. And each time, Washington will be forced by law to cease its contributions to that agency.

The United States would not actually lose its membership by stopping its financial support – at least not for a good long while – but it would lose all practical influence on these agencies, which do a great deal of the work of running the world. It would be a diplomatic disaster for Washington…

I thank Sean Brockelbank for the pointer.