The only possible way to answer this briefly is to say that there was internal resistance to some degree during this time. The degree of internal resistance ebbed and flowed, particularly since there were different levels of official tolerance of dissent during these years.
After Stalin died, there some loosening of controls as Khrushchev criticized Stalin and engaged in "deStalinization." This inspired some dissidents to push for greater reforms. Some famous dissidents of this time were Alexander Solzhenitsyn and Boris Pasternak. The government, however, did not allow much in the way of dissent and soon shut this down.
There was another wave of dissent in the 1970s. This wave centered around a demand for more human rights in the wake of the easing of Cold War tensions with the West. Some of the best-known dissenters of this era were Jews like Natan Sharansky who wanted to be allowed to leave the USSR and go to Israel. This effort, too, was suppressed.
So, there was always some degree of dissent against the Soviet system, but it was never given much scope to express itself.