With Morsi's Muslim Brotherhood government preoccupied with battling for survival, the fear is the jihadists will use the turmoil to step up attacks on Israel, endangering Egypt's landmark 1979 peace treaty with it.
Egyptian militant sources say there are more than 1,000 armed jihadists, split between several groups linked by varying degrees to al-Qaida, currently operating in the forbidding wasteland of Sinai.
Leaders of Bedouin tribes in Sinai say the jihadists have stepped up recruiting in recent weeks, suggesting that major operations may be planned.
But although terrorist attacks against Israel launched from Sinai could jeopardize the peace treaty, there's evidence that Sinai's becoming a major problem for the Cairo government as well, and one that Morsi ignores at his peril.
The security vacuum in Sinai, a vast area of mountains and desert that lies between the Suez Canal and Israel, stemmed from the pro-democracy revolution in Egypt in early 2011 that ended the three-decade dictatorship of President Hosni Mubarak.
The Egyptian government never did have much control over the peninsula, where the two countries have fought four wars, but whatever vestige of law and order that remained collapsed with the 2011 uprising.
Disgruntled Bedouin tribesmen, long neglected during the Mubarak era, drove out the Egyptian police and many joined the jihadists who flooded in, heavily armed with weapons plundered from Libya.
Israel captured the peninsula in the 1967 war and relinquished it in 1979 as part of the peace agreement with Egypt, Israel's first with an Arab state and the linchpin on its security strategy.
That limited Egypt's military presence, which makes it difficult for Cairo to crack down on the militants and criminal gangs operating there.
With Israel's approval, Morsi finally deployed military reinforcements there in mid-May after militants kidnapped seven police officers, and to block infiltration by hard line Palestinian militants from the neighboring Gaza Strip ruled by the fundamentalist Hamas movement.
Sheikh Nabil Naim, leader of the Egyptian Islamic Jihad group, told the pan-Arab Asharq al Awsat daily, published in London, in May that the Brotherhood in Cairo maintains links with jihadist organizations in Sinai.
The word is that Morsi's people do not pursue the jihadists with any vigor because they believe the Brotherhood may need their support to crush its political opponents inside Egypt proper one day.
That goes some way to explaining Morsi's apparent reluctance to send troops into Sinai to hunt down the kidnappers of the police officers.
He repeatedly advocated negotiating with the militants even when there was clear public pressure for "cleansing the Sinai" of the jihadists even at the expense of military casualties.
According to the social media in Egypt, there's a growing demand for amending the peace treaty to give Egyptian forces wider sovereign rights in Sinai and a free hand to crush the jihadists.
The fear is that terrorist attacks on Israel, could drag Egypt into armed conflict with the Jewish state, which has defeated Egyptian forces in all of the four wars they fought in 1948, 1956, 1967 and 1973.
The Egyptian military, which has benefited greatly from U.S. military aid since the 1979 treaty that was brokered by President Jimmy Carter, does not want to go to war with Israel again.
An analysis by Israel's Institute for National Security Studies released Sunday said that despite the recommendation by Egypt's military commanders for cracking down forcefully on the Sinai Jihadists, Morsi insisted on negotiations to free the policemen.
These resulted in their eventual release, but it's deepened what analysts see as a growing rift between Morsi and Egypt's military, whose power he has sought to diminish, as the jihadists continue to challenge Cairo's control.
"There are two prevalent fears expressed on the Egyptian social media in relation to Israel and Sinai," the institute observed.
These are that "Sinai will continue to be a fertile breeding ground for jihadist militias, whose activities could lead to an Israeli decision to reoccupy Sinai ... or an open-ended military operation that would violate Egyptian sovereignty.
"There is therefore a growing demand for a comprehensive Egyptian military operation in Sinai to cleanse the area of these terrorist elements."
Notable deaths of 2014 [PHOTOS]