Unfortunately, there is nothing but wishful thinking on which to base that belief.
Mothers speak with pride of their suicidal sons; crowds dance in the streets celebrating the death of the "infidel"; schools teach hatred for the Jews to little children ...
We have yet to hear from peaceful "majority". It seems that any man on the street who is asked about his views spews venom and hatred. I tend to believe that if the "islamists" got out of the neighborhood, they'd leave a ghost town behind.
Recent polls conducted by Islamic scholars in the area report that over 60% believe the ultimate goal for Palistinians is not a co-existence w/ Israel in a negotiated two state solution, but rather a Trojan Horse settlement whereby ultimately they can exterminate the Jewish State from within.