A last-ditch American effort to head off a Palestinian bid for membership in the United Nations faltered. President Obama tried to qualify his own call, just a year ago, for a Palestinian state. And President Nicolas Sarkozy of France stepped forcefully into the void, with a proposal that pointedly repudiated Mr. Obama’s approach.

The extraordinary tableau Wednesday at the United Nations underscored a stark new reality: the United States is facing the prospect of having to share, or even cede, its decades-long role as the architect of Middle East peacemaking.

Even before Mr. Obama walked up to the General Assembly podium to make his difficult address, where he declared that “Peace will not come through statements and resolutions at the U.N.,” American officials acknowledged that their various last-minute attempts to jump-start Israeli-Palestinian negotiations with help from European allies and Russia had collapsed.

American diplomats turned their attention to how to navigate a new era in which questions of Palestinian statehood are squarely on the global diplomatic agenda. There used to be three relevant players in any Middle East peace effort: the Palestinians, Israel and the United States. But expansions of settlements in the West Bank and a hardening of Israeli attitudes have isolated Israel and its main backer, the United States. Dissension among Palestinian factions has undermined the prospect for a new accord as well.

Finally, Washington politics has limited Mr. Obama’s ability to try to break the logjam if that means appearing to distance himself from Israel. Republicans have mounted a challenge to lure away Jewish voters who supported Democrats in the past, after some Jewish leaders sharply criticized Mr. Obama for trying to push Israel too hard.

The result has been two and a half years of stagnation on the Middle East peace front that has left Arabs — and many world leaders — frustrated, and ready to try an alternative to the American-centric approach that has prevailed since the 1970s.