Since the survey doesn't appear on their webpage we have to take the article at face value. Before leaping to conclusions it might be a good idea to know specifically which questions were asked and which circumstances were detailed. And although certain people here consider that they know more than Israeli citizens it's not certain what weapons we do have.
Ex-FM Lieberman: Firebomb attack in Jerusalem a reminder that norm is Arab terror against Jews (Haar
from the article: Poll: 72% of Israelis back use of nuclear arms in certain circumstances