This posing of the question of public support as if either you have it or you don't is simplistic. Even the results of the elections that Hamas won did not suggest that they were supported by more than 45%, with Fatah getting over 40%. If your rhetorical point is that they don't have 100% pubic support, that just puts them in the same position as every single democratically elected government in any country in the whole of history. You mention with approval the idea that Hamas should "take responsibility". Does this mean anything at all, in terms of realistic policies they could pursue to change the situation in Gaza?
One dead, three injured in Northern Arizona University shooting (DPA)
from the article: What Hamas is really afraid of