Short answer: Mao was never in any danger of being purged. He did loose most of his responsibilities for economic policy after the Great Leap, and focused more on cultural matters and building up his cult of personality after 1960. This put him in a good position to launch the Cultural Revolution in 1966, which was in part an attack on his own party to restore his position.

Longer answer: Mao was never all-powerful, and even before the Great Leap there were arguments about policy between people in leadership. The most common divide was between Mao and the left-leaning “go fast” group and the more conservative (or practical) group led by Liu Shaoqi. What does going fast mean? Lots of things, but mostly a quicker transition to Communism through things like eliminating private enterprise, and communalizing agriculture but also a certain distrust of Soviet style central planning and emphasis on heavy industry and expertise as opposed to mass mobilization. The Great Leap was a disaster, and a Maoist disaster. Rapid establishment of communes and urban policies like the backyard steel furnaces were a huge disaster leading to collapsing production and mass starvation.

That said, the Leap was not all Mao’s doing. Plenty of other leaders supported it, for whatever reasons, and parts of it were popular with the masses. Being able to eat all you wanted in the commune canteen, not having to cook (a lot of women’s work was communalized), joining an advanced production collective to get cheap fertilizer, these were all popular. People (and officials) also got swept up in the mass hysteria of the movement. (See the backyard furnace scenes of the film/novel To Live for a dramatization). Even the other members of leadership did not realize how bad things were until they personally went down to the provinces to check things out. Almost everyone was reporting wildly inflated production numbers because -everyone else- was reporting insane numbers. This is not to absolve Mao of blame, but to point out he was not the only impetus for the disaster.

Mao was definitely criticized for his role in the mess. He made a self-criticism at the Seven Thousand Cadres Conference in early 1962. On the other hand, Peng Dehuai was purged for criticizing the Leap (and implicitly Mao) at the Lushan Conference in 1959. Mao was a potent force even when sidelined. Also, the dispute over the Great Leap was in part about who was responsible for the mistake, but also a about the continuing struggle over what direction the revolution should be taking. Peng Dehuai was convinced by his experiences in the Korean War that the Chinese military needed to be modernized and professionalized. He was replaced by Lin Biao, who was more loyal to Mao and was much more in favor of People’s War.

In 1962 Mao launched the Socialist Education Movement. He claimed that the Great Leap had failed because class enemies had seized control of the party at the lower levels. (Walder pg 189) This was supported by Liu Shaoqi, who was fine with sending work teams down to investigate, struggle with and purge local cadres. Really nobody was opposed to the Maoist method of “take class struggle as the key link” or “putting politics in command”, they just emphasized it less than Mao himself did.

It was between the Great Leap and the Cultural Revolution that many parts of the Mao cult came into final form. Quotations from Chairman Mao came out in 1964. The cult of Lei Feng starts in 1963. Mao’s wife, Jiang Qing started to get involved in politics at this time. All of these where things Mao did while sort of sidelined in economic policy making but that would put him in a good position to launch the Cultural Revolution in 1966. You can’t purge those disloyal to Chairman Mao thought from above and below unless everyone knows what that is. Still, even Mao was less in control of the CR than he thought. He launched it as a purge, but it quickly got out of control as people all over China took advantage of the opportunity to “bombard the headquarters”.

Sources

Mühlhahn, Klaus. Making China Modern: From the Great Qing to Xi Jinping. Reprint edition. Harvard University Press, 2019.

Saich, Tony. From Rebel to Ruler: One Hundred Years of the Chinese Communist Party. Harvard University Press, 2021.

Walder, Andrew G. China Under Mao: A Revolution Derailed. Reprint edition. Harvard University Press, 2017.