Basically, in the beginning many voices in the CCP and Deng Xiaoping himself were sympathetic to the protests, but as they dragged on and more radical voices gained ground with demands like opening the country and introducing free elections, the tides in the upper (and lower) branches of the CCP turned against the reformers.
It is also interesting to note that while the reformers have been mostly side-lined since then, and Xi especially is a hard-right hardliner, the party is still at least paying lip-service to reformers. - For example one of the key policy goals of the last 5-year plan was to continue to develop Hong Kong into a global financial centre and broadly liberalize the chinese economy.