Abdallah's demise would probably mark the end of nearly 60 years of rule by the sons of King Abdulaziz, the tribal warrior who founded the modern kingdom in 1932, and the accession of his grandsons to the throne.
That raises questions about the future of the kingdom in a profoundly changing world and a possible realignment of its strategic policies, which many believe is under way as U.S. power in the Middle East is on the wane.
The U.S. focus on its abundant shale oil reserves will eventually make it self-sufficient in energy production, ending its dependence on cheap gulf oil since World War II, much of it from Saudi Arabia.
That will dramatically alter Washington's strategic outlook, which is already shifting from the Middle East to the Pacific and China's economic and military challenge.
At the same time, the monarchy is struggling to contain the 22-month-old surge for democratic reforms across the Arab world that has toppled presidents in Egypt, Tunisia, Yemen and Libya and could bring down a fifth in Syria.
No Arab monarchy has yet succumbed but worsening tensions between them and Iran has magnified the crises that grip them.
Saudi Arabia, birthplace of Islam, leads these Sunni-dominated states against Iran, which is ruled by the breakaway Shiite sect, in a deepening rivalry that harks back to a religious schism that split Islam in the seventh century.
Against this menacing backdrop, reports that Abdallah was at death's door caused tremors across the region.
The London-based pan-Arab daily Asharq al-Awsat reported that King Abdallah, who ascended the throne in 2005, was in a coma and considered clinically dead a week after his Nov. 18 surgery at the King Abdulaziz Medical City in Riyadh.
The state-of-the-art hospital is controlled by the Saudi Arabian National Guard, a powerful mechanized tribal force independent of the military and whose mission is the protection of the royal family.
The 100,000-strong Guard is commanded by one of Abdallah's sons.
Asharq al-Awsat quoted hospital officials as saying Abdallah's heart, lungs and kidneys weren't functioning and that doctors had used "electric shocks to stimulate his cardiac muscles."
But the royal court insists the 11-hour operation, reportedly to tighten a ligament in his back, was completely successful.
The official Saudi Press Agency reported that Crown Prince Salman, who would become monarch if Abdallah dies, "reassured" a Cabinet meeting Monday by saying the monarch was "well and in good health."
Salman is Abdallah's brother and 13 years his junior. Abdallah appointed him in June after the death of Crown Prince Nayef bin Abdulaziz.
But Salman has also been reported to have health problems. Simon Henderson, an expert of gulf politics at the Washington Institute for Near East Policy, says Salman "is widely reported to be in a poor mental state."
If that's the case, his accession if Abdallah dies must be questionable.
Abdallah's health has been declining for several years and he's been hospitalized several times.
A succession of Abdulaziz's sons has ruled since his death in 1953. But now the surviving sons are all in their dotage and the big question is when will the old king's grandsons finally take over.
"The odds are now high that Salman's successor will come from the third generation of princes," the U.S. global security consultancy Stratfor observed.
"There are only a few second-generation princes alive who have the qualifications to become crown prince" under Salman, it noted.
Kings traditionally have been chosen by the royal family, which has several rival factions. But Abdallah decreed a succession law in 2006 that's supposed to elect the king and crown prince.
"The problem is that this system assumes a basic democratic tradition among the royal family; such a tradition has never existed and there is no reason to assume that one will exist in the near future," Stratfor cautioned.
"As a result there will be an added potential for rifts among the various House of Said clans and with them the risk of instability in the world's biggest oil producer."