In an extraordinary press conference, President Bill Clinton and the three emissaries he dispatched to Haiti wove a fascinating narrative of how the deal to avert an invasion was struck -- and was nearly undone. At a noon White House press conference, Clinton admitted that he'd given former President Jimmy Carter, former Joint Chiefs of Staff chairman Colin Powell and Sen. Sam Nunn a 3 p.m. EDT deadline yesterday to clear out, then reluctantly let the talks creep on even as he ordered Air Force fighter planes toward Port-au-Prince. By Carter's account, turmoil ensued when Gen. Philippe Biamby -- now thought to be the most powerful junta leader -- received a report about the aircraft: "They thought [the delegation] was a trick to keep all the military commanders in the same room while an invasion took place," said Carter. "The thing was about to break down." The deal-saver was a trip to Haitian President Emile Jonaissant's residence, where the aged Haitian head of state agreed to a plan. SO, WHAT'D THEY AGREE TO? Lt. Gen Raoul Cedras and other Haitian military leaders will be granted amnesty without being forced to leave the country. Clinton defended the agreement, saying the U.S. had agreed to such provisions in the Governor's Island accord last year.