Hamas doesn't have widespread support. They pretended to be a reformed, moderate, responsible party who no longer wanted to be seen as the extremists that they used to be. Because of this, they won a very slim plurality in the 2006 election and then indefinitely postponed the following election. I don't think I'm alone in assuming that quite a bit of what support they do have from the Palestinian people is from either implicit or explicit coercion. Otherwise, support is likely from Hamas daring to retaliate against Israel for mistreatment up to murder of innocent Palestinian civilians over the decades.
Hamas fucking sucks. They just happen to be the only leadership left for the Palestinian people because Hamas has tricked the people into giving them power and they've had a death grip on it ever since, preferring to let Palestine get wiped off the map rather than lose that power.