I am unsure if you meant opposition from within the Soviet Union or from outside. However there was great pressure inside the Soviet Union to stop its eventual decline. It was headed by more military conservatives, led ultimately by the KGB Chairman, Vladimir Kryuchkov along with other brass in the military as well. They attempted to stage a coup that is described best in the quote below from coldwar.org:

Finally, the situation came to a head in August of 1991. In a last-ditch effort to save the Soviet Union, which was floundering under the impact of the political movements which had emerged since the implementation of Gorbachev’s glasnost, a group of “hard-line” Communists organized a coup d’etat. They kidnapped Gorbachev, and then, on August 19 of 1991, they announced on state television that Gorbachev was very ill and would no longer be able to govern. The country went into an uproar. Massive protests were staged in Moscow, Leningrad, and many of the other major cities of the Soviet Union. When the coup organizers tried to bring in the military to quell the protestors, the soldiers themselves rebelled, saying that they could not fire on their fellow countrymen. After three days of massive protest, the coup organizers surrendered, realizing that without the cooperation of the military, they did not have the power to overcome the power of the entire population of the country.

It was a time of flux and ultimately the people of Russia tasting the freedoms with perestroika and glasnost refused to return to the days before, and protested. Within days of the coup failing, the Soviet Union fell. The people involved in the coup, Kryuchkov included, were arrested.

This is a quick and dirty explanation, however some good information can be acquired from David Remnick's amazing work Lenin's Tomb and I have heard that Stephen Kotkin's Armageddon is great as well.