The growing unrest amongst students, people and the political elite was caused by divisions within the party.

Deng Xiaoping believed in the need of absolute authority.

The death of general secretary Hu Yaobang (a reformist) fueled anxieties about the future of the country.

Foreign-backed regime change??

Deng was actually in the middle between the hardliners and reformists, from accounts I've read. He wasn't officially head of the party anymore, and there was stalemate for a few days about how to handle the protests before Deng finally weighed in with 'enough is enough'.