(Changes dateline, adds background) By Matt Spetalnick and William Maclean WASHINGTON/DUBAI, April 8 (Reuters) - Addressing the United Nations General Assembly in September, U.S. President Barack Obama declared the pursuit of Israeli-Palestinian peace one of the two main U.S. foreign policy priorities for his second term. Fast-forward to today, the Obama administration faces a stark choice: expend more energy on a faltering peace process or absorb the hit to an already-troubled record in the Middle East and walk away from negotiations. Secretary of State John Kerry, who met Obama on Tuesday for a "reality check," says he hopes both sides will work with U.S. mediators to "find a way back." But as optimism fades, many inside and outside the Middle East warn **w is **t the time for a U.S. diplomatic failure in the region.