It is no secret that Fatah has long been trying to get rid of Fayyad who, its representatives argue, had been imposed on the Palestinians by the Americans and Europeans.
Abbas and Fatah have been trying for years to replace Fayyad with one of their own so that they could regain control over the Palestinian Authority's finances.
The US and most Western donors have repeatedly made it clear to Abbas that removing Fayyad from his post would prompt them to reconsider financial aid to the Palestinians.
Fatah leaders in the West Bank were hoping that the street protests would force Fayyad to resign. But the prime minister's refusal to succumb to the immense pressure (and threats) has left most of these leaders deeply disappointed.
For Fatah, the public outcry over the high cost of living provided a good opportunity to resume its efforts to remove Fayyad.
As soon as protesters took to the streets in a number of West Bank cities last week to demand the resignation of Fayyad, Abbas, who was in Cairo, declared that the "Palestinian Spring" had begun and that he supported the "just demands" of the demonstrators.
Abbas's comment was seen as a green light to the protesters to take to the streets and demonstrate against Fayyad.
For several days, Palestinian Authority security forces had been instructed not to prevent the protesters from burning posters and effigies of Fayyad. The security forces also did not interfere as long as the protesters chanted slogans denouncing only Fayyad as an American and Israeli agent.
Some Palestinians believe that the protests actually served the interests of Abbas and Fatah, who have been widely accused of standing behind -- or at least encouraging -- the demonstrations calling for the ouster of Fayyad.
Palestinians noticed that in many cities, Fatah activists were organizing and leading the anti-Fayyad protests.
The unprecedented attacks on Fayyad stood in sharp contrast to the way the Palestinian Authority leadership had reacted in the past to criticism of Abbas.
Several Palestinian journalists and bloggers have been arrested since the beginning of the year by Palestinian security forces for publicly criticizing Abbas.
Abbas clearly had no problem as long as Palestinians were chanting slogans against Fayyad and hurling shoes at the prime minister's posters in city centers.
But as soon as some of the protesters began directing their criticism also against Abbas and demanding an end to the Oslo Accords, Palestinian Authority officials warned that "outside elements" had infiltrated the ranks of the protesters in order to serve "foreign agendas."
The "outside elements," the officials claimed, were linked to Israel, Hamas, Iran and all the enemies of the Palestinians.
Abbas, who did not meet once with Fayyad during the crisis, was hoping that the demonstrations would send a message to the Americans and Europeans that the time has come to replace the prime minister. Instead of working with Fayyad to tackle the crisis, Abbas and his top aides preferred to spend the week in India.
However, when Fayyad announced a series of austerity measures to alleviate the economic hardships, Abbas's office rushed to announce that Fayyad did so "on the instructions of the Palestinian president" -- himself. Abbas was now trying to take credit for complying with the demands of the street.
Abbas and Fatah were also hoping that the protests would achieve other goals.
First, they were hoping that the scenes of anarchy and lawlessness on Palestinian streets would put pressure on many Arab countries to resume financial aid to the Palestinian Authority. Some Gulf countries are reported to have cut off aid to Abbas's authority because they feel that he is not serious about combating corruption and implementing major reforms.
Second, Abbas and Fatah were hoping that the protests would persuade the Americans and Europeans to increase financial aid to the Palestinians.
Third, Abbas was hoping that the demonstrations would prompt the Americans and Europeans to intensify pressure on Israel to accept his preconditions for resuming the peace process: a full cessation of settlement construction and recognition of the pre-1967 lines as the future borders of a Palestinian state.
Fourth, Abbas and his advisors were hoping that the protests would put the Palestinian issue back at the top of the international community's agenda, especially at a time when the Iranian threat appears to have stolen the limelight.
Fifth, Abbas was hoping that by blaming Israel for the economic woes of the Palestinians, he would be able to divert attention from his failure to produce any significant achievement for his people ever since he came to power in 2005.
The 77-year-old Abbas is about to enter his eighth year of his four-year term in office and has shown no sign that he is willing to step down and pave the way for the emergence of new leaders.
The recent protests in the West Bank over the economic hardships do not signal the beginning of a "Palestinian Spring." Rather, they are seen by many Palestinians in the context of the ongoing behind-the-scenes power struggle between Palestinian Authority President Mahmoud Abbas's ruling Fatah faction and Prime Minister Salam Fayyad.