KALANDIA, West Bank — It is far from clear what will happen when the Palestinians go to the United Nations next week to seek recognition of statehood. But the initiative is engaging a Palestinian public that had become deeply cynical after 20 years of intermittent Israeli-Palestinian peace talks.

Many Palestinians here in this refugee camp between Ramallah and Jerusalem said that they were excited by the prospect of their territory’s being declared a state, but that they recognized that it would not immediately improve their lives. Instead, they braced for possible punitive steps by the United States and Israel.

“Abu Mazen is doing a good thing, but the reactions could be bad,” said Khairiyya Abd al-Rahman, 66, a matronly resident of the refugee camp, using the popular name of the Palestinian president, Mahmoud Abbas.

Going to the United Nations remains a high-stakes gambit for Mr. Abbas. Whether it succeeds or fails, the Palestinians’ frustration is likely to increase if their reality does not change. And while many Palestinians say they do not foresee the eruption of a third uprising, they warn that something is bound to give eventually if there is no measurable progress.