There are a number of Salafi-jihadist groups that operate inside Gaza, including, but not limited to: Jaysh al-Islam, Fatah al-Islam, Abdullah Azzam Brigades, Jaysh al-Ummah, and the Mujahideen Shura Council in the Environs of Jerusalem. Both Fatah al-Islam and Abdullah Azzam Brigades have ties to al-Qaeda. The aforementioned Mujahideen Shura Council in the Environs of Jerusalem, an umbrella-group of several Gaza-based Salafi-jihadist groups, has taken sides with the Islamic State in the jihadist infighting and is even rumored to have pledged allegiance to them. These groups are all relatively small, but maintain a steady rank of fighters.
All of these groups mentioned (and many others) not only oppose Israel and share a global jihad view, but are also vehemently opposed to Hamas. None of these groups have the size, strength, financing or capabilities like Hamas, but they do constitute a very real threat for Palestine and Israel. In this Washington Institute for Near East Policy report in 2009, "...activists from Jaish al-Islam and Fatah al-Islam joined together to plan an attack on the Middle East Quartet's special envoy and former British prime minister Tony Blair during his Gaza visit in July 2008. The plan involved snipers and explosives targeting Blair and his entourage. Fortunately, Israel obtained high-quality intelligence about the plot and passed it along to Blair before he traveled to Gaza. He subsequently canceled the visit, thus thwarting the attack".
A more recent example of a threat posed by these groups is the video posted above, in which ABM, a Sinai-based group but is rumored to operate in Gaza, launched rockets towards Israel. Or the Abdullah Azzam's Gaza Wing, Yahya Ayyash Brigades, launching rockets into Israel recently.
Hamas seems to have mixed feelings about Salafi-jihadist groups. While on one hand they see them as a threat to their control over Gaza, they ultimately see them as a vital ally against Israel on the other. This can be seen by them being complicit in their firing of rockets, but take a hardline against them in other times. While Hamas sees themselves as the "Palestinian Resistance against Israel", they potentially lose support and recruits when they are forced to negotiate with the aforementioned state. This could subsequently pose as a real concern for Hamas, as they must juggle both trying to govern the Gaza Strip and put up a viable resistance towards Israel. And while these Salafist-jihadist groups ultimately oppose Hamas, they have worked together militarily.
People of Gaza:
The people of Palestine have recently taken a poll and voted against the use of violence against Israel. While most still supported "reclaiming the entirety of the historic lands of Palestine", most Gazans polled (around 70%) supported Hamas accepting and honoring a ceasefire with Israel. Furthermore, almost 60% supported a unity government with Mahmoud Abbas and renouncing violence. Still even further, almost 73% said that popular resistance had a "positive impact".
With this poll, it most definitely shows most Gazans oppose Hamas and their actions against Israel; interestingly enough, most Gazans polled also wanted more job opportunities from Israel. This poses some serious implications for not only Hamas, as their support is waning both domestically and abroad, but the Salafi-jihadists, as well. If the people of Gaza are against the use of force against Israel by Hamas, it stands to reason that would not support violence perpetrated by these Salafist groups. At the same time, however, support for Salafi-jihadist groups from former Hamas, Fatah, Palestinian Islamic Jihad members and/or disheartened Palestinians is and has been growing in recent years. While most everyday, average Gazans/Palestinians will continue to oppose violence against Israel, support for Salafist-jihadist groups could grow even further in the event of Hamas declining even further or increased propaganda and recruitment operations by al-Qaeda and/or the Islamic State or independent groups.
Having said that, the Islamic State could begin to operate more in Gaza to try and counter al-Qaeda's operations there and to gain more support and fighters for its caliphate project.
Most people in Gaza, despite currently being bombarded by Israel as a result of Hamas and Salaf actions, do not support violence against Israel. However, the small Salafist-jihadist groups operating in Gaza continue to operate and maintain a healthy rank of fighters. Even further, their support from disheartened former Hamas, Fatah and Palestinian Islamic Jihad members and hardline/radical Palestinians is growing in light of the decline of Hamas.
If Israel goes ahead with a large-scale ground incursion of Gaza to remove Hamas like it said it might, it may prove to serve as a catalyst for Salafi-jihad support and activity in Gaza.