But many experts call the campaign a failure.
"They did not get the ... votes at the Security Council and so I think that bid basically has failed," said David Makovsky, director of the peace process project at the Washington Institute for Near East Policy, a think tank.
The Palestinians had to get nine votes from the 15 Security Council members, but too many said they would abstain or oppose the bid. Even if they had succeeded, the United States had made it clear it would veto the bid.
The United States and Israel insist that only an Israeli-Palestinian accord can lead to the creation of a Palestinian state.
The Palestinians may be holding back because they do not want to further risk their relations with President Barack Obama's administration, Makovsky told AFP.
Philip Wilcox, a scholar with the Middle East Institute and former US diplomat with special responsibility for Middle East affairs, also called the Palestinian bid a "failure" -- for now.
"I don't think they will ask for a vote unless they are sure to get nine votes," Wilcox said.
The Security Council's new members committee could not agree on a united recommendation on the Palestinian application and for the past month the Council has been waiting for a sign from the Palestinian leadership on their next move.
Abbas could also decide to seek a super-observer status at the UN General Assembly where a majority is virtually guaranteed but the prize would have much less status than full membership.
Palestinian diplomats at the United Nations say they are waiting for instructions from Ramallah. Western envoys at the UN say they have been told not to take any action until Abbas decides.
"We are really not sure what the Palestinian strategy is and whether they have one," one senior Western diplomat said.
Vitaly Churkin, Russian envoy to the UN and president of the Security Council for December, indicated that he too is in the dark, when asked at a press conference on Friday.
He said the council is still waiting for the Palestinians' decision, but a vote could be "very quickly" organized if asked for.
The Palestinian envoy to the United Nations, Riyad Mansour, said this week that the leadership was "unwavering" in its determination to seek UN membership.
Mansour often tells how Israel's bid for UN membership was turned down when it was voted by the Security Council in 1948. Israel only got its place in 1949.
With no legal or administrative deadline to force Palestinian action now, Makovsky said the Palestinians could return to the charge in 2012. "Remember, this is the Middle East and even when people don't have a grand strategy you cannot guarantee that it will not come up in the future."