I don't really understand how you can conduct a poll in a place like Gaza, but the Palestinian Center for Policy and Survey Research says they can do it. Here's one result from their latest survey:
After nearly a year of the most brutal pummeling imaginable, only 28% of Gazans still think Hamas can win the war. But still: 28%!
In other results, Hamas has lost a bit of support but is still the most popular single faction in Gaza. And Gazans really, really don't like the United States. I wouldn't be surprised if we poll lower than Israel.
On a side note, there's also this:
This is something I've been following for a while, and this survey seems to confirm that food shipments are improving—at least in southern Gaza. PSR doesn't do fieldwork in northern Gaza, so we have nothing on that one way or the other.