Lets look at the facts.
According to Wikipedia,
the election was close:
Of the Electoral Lists, Hamas received 44.45% and Fatah 41.43%[1] and of the Electoral Districts, Hamas party candidates received 41.73% and Fatah party candidates received 36.96%.[1]
Palestinian Public Opinion Polls - 2006 exit polls:
Survey Research Unit
Survey Research Unit
(5) The Peace Process and Electoral Behavior
Findings also show that 69% of those who place the peace process at the top of their priorities voted for Fateh while only 19% voted for Hamas. But findings show that only 9% placed the peace process at the top of the list of priorities which, needless to say, explains the devastating blow Fateh received on election day.
...Palestinian vote for Hamas on the day of elections should not however be interpreted as a vote against the peace process. About 60% of all voters identified themselves as supporters of the peace process while only 17% saw themselves as opposed to it and 23% saw themselves somewhere in the middle between opposition and support. Moreover, the vote does not mean that all those who voted for Hamas are opposed to the peace process. To the contrary, findings show that 40% of Hamas voters in fact support the peace process and only 30% oppose it. Moreover, abut one third of Hamas voters support collection of arms, the implementation of the Road Map, and the recognition of Israel as a Jewish state in a two-state context. Findings clearly show that a majority of Fateh and the combined voters of other lists support all there elements of the peace process (see table below).
And, from the same link:
(6) Corruption and Lawlessness and Electoral Behavior
Findings clearly show that what damaged Fateh’s electoral chances was the decision by a large percentage of voters (25%) to make the ability of the list or faction to fight corruption the most important consideration when voting for the various lists. What made things worse for Fateh was the belief of an additional large percentage of voters (37%) that addressing lawlessness and chaos is the central issue that determines people’s vote. The fact that 75% stated that they personally do not feel safe and secure in their homes only made things worse for Fateh.
This is how Hamas benefited from this:
71% of those who considered corruption the most important consideration in voting voted for Hamas and only 19% for Fateh and 11% for the other lists.
Support for Hamas among those least safe and secure reached 56% and for Fateh 31%. By contrast, vote for Hamas among the most safe and secure dropped to 35% while increasing to 53% in the case of Fateh. Other lists benefited also from the absence of safety and security as the percentage of support for these lists increased among the least safe and secure and decreased among the most safe and secure.
These are the reasons Hamas was looked at more favorably by the Palestinian electorate and even then it was close. To make sweeping generalizations that this indicates support for the Jihadist movement based on Hamas' victory is inaccurate and unfair to the Palestinians.
Next, let's look at Palestinian attitudes in 2007:
Survey Research Unit
Findings of the second quarter of 2013 show a widespread state of frustration and pessimism. 80% believe that the West Bank-Gaza Strip split is either permanent or long term. Less than one third of the public views the PA, in its two incarnations in the West Bank and the Gaza Strip, as an accomplishment for the Palestinian people. Moreover, less than a third believes that a Palestinian state will be established in the next five years. In fact, a majority, while continuing to support the two-state solution, believes that it has become impractical due to settlement expansion. Perhaps for these reasons half of the public believes that its leadership from the beginnings has been a failed one.
...Findings also indicate public opposition to ideas brought by US Secretary of State John Kerry for restarting peace negotiations: without preconditions, with an economic package, and with focus on security and borders. The public is also opposed to several alternatives to negotiations such as return to an armed intifada, dissolution of the PA, and abandonment of the two-state solution in favor of one-state solution. But the public supports going to international organizations, especially to the International Criminal Court (ICC), despite its fears that such a step would bring about financial sanctions and the perhaps the collapse of the PA.
What this indicates to me is that the current state of governance and the election precipitating it has far less to do with a simplistic "pro-intifada" meme (as claimed by the Pro-Israel faction) and more to do with complicated domestic issues and with a losing hope for self determination.
Perhaps the media has much to do with this perception of the Palestinian people.