With Yasser Arafat, 75, thought to be near death, Abbas, a founder of the Palestinian Liberation Organization, is a leading contender to become president of the 3.6-million Palestinians. But the doubts Palestinians have about Abbas illustrate the great dilemma of the post-Arafat era: finding a leader flexible enough to be accepted by Israel and the United States, yet strong enough to convince Palestinians that he is not selling them down the river.