I want add this, third answer to clarify some issues with terminology and how the things were run in the USSR.
First of all I want to point out that I have learned from the Internet that in the USA there is common sentiment of some distrust of the government, a dichotomy between "we" and the government. But in the USSR there was no such dichotomy. The government was "we". The system of feedback in the Soviet system was overwhelming. If you wanted something concrete done and it was uncontroversial, you would have it done, even if it was formally illegal or against the regulations. A petition usually was more than enough. A petition from an initiative group or a merited citizen was excessive. So, people generally had no grounds to criticize the government: if someone had good arguments for something changed, it would be changed. Any idea would be heard. Coming up with ideas was encouraged. Criticizing the government thus would be like criticizing themselves. At worst they would blame some certain official who barred the idea.
The plaque says "Here works the member of the Supreme Council of the Ukrainian SSR".
The system of government in the USSR closely followed the people's mentality and their understanding of what is right. But what changed with time is that while in the early USSR the system mostly followed the mentality of the whole people, towards the end of the USSR the main reference base became ethnic Russians and ethnic Russian mentality.
It is also worth to note here that many Communist moral principles as implemented in the USSR were borrowed from the moral of the Russian Orthodox Christianity and pre-Communist Russian mentality. Simply put one can argue Communism in Russia was just Christianity without Christ, the similar way some argue the modern ideology in China is just Confucianism painted red and the American ideology is just disguised Protestantism. Thus these principles were quite uncontroversial among the general public.
That said, I would say that Socialist principles and Socialist understanding of justice were quite universally accepted, like say "democracy" principles are accepted in the USA. There were people who would advocate for Capitalism or Monarchy but they were fringe, like those who advocates for Communism or neo-Nazis in the USA.
So even those who criticized the social order of the USSR would usually bring arguments of the kind that the things were wrong because they did not follow the principles of Socialism. Compare medieval Europe here: there, you usually would not call to replace Christianity with some other religion, but would say this and that bad thing is un-Christian.
So if there were things which were disliked, the people would not call to overthrow the whole social order, but to improve the existing one, similarly how in the USA one would not call to overthrow Democracy because of police misbehavior, but would rather say the police's bad behavior was undemocratic.
Another thing to understand is that the Communist party was not really a political force in the USSR. It was rather a structure of the state. So the very question about whether one supports the rule of CPSU (which was reflected in the constitution) would look very strange, like if an American was asked whether he is content with the idea of being ruled by the Congress and Senate. Well, maybe someone would say he would prefer a queen, but this would not be quite a common answer. More often you would hear the wishes that bad and corrupt people should not be accepted into the party.
A more concrete question would be whether one supports the current government and certain personalities in it. Here, the answers could vary a lot. If you ask somebody in the US whether he supports Democracy and whether he supports Obama, the results will be completely different. Similarly, in the USSR there were a lot of people who disliked this or that minister or party official. Among the USSR leaders the least popular were Khrushchev and Gorbachev.
But here again, the majority of people would be loyal. This is because most people are unpolitical. Another feature of Russian mentality is that there a widespread type of people who would support any government irrespective of its policy, so they now support the Capitalist government the same way they supported the government under the USSR. In absence of central media who criticized the government, the popular approval of any current government in the USSR was greater than approval rating of the most of the US presidents.
That's why the whole thing of transition towards Capitalism was done from top to bottom, by the incumbent government and masked with Leninist rhetoric. When the majority of the people realized we were going in a wrong direction, it was already too late: Gorbachev had made himself invulnerable by becoming the president. Before him all Soviet leaders could be ousted at any time, the way it happened with Khrushchev, but the president office introduced by Gorbachev had a fixed term, and the impeachment procedure was made highly difficult. Thus the August coup of 1991 followed.
Now, last thing to clarify. One can ask, what Russians thought about better economic development in the Capitalist countries compared to the USSR, higher quality of life etc.
Here the answers can vary. The official propaganda said the following things: it is not that good in the West for the poor; the wealthy Capitalist countries exploit the poor Capitalist countries, that's why they are rich etc. There were people who believed this propaganda and those who did not.
Now, among those who did not, the most common explanation would be along the lines "it is because we (Russians) cannot work well, because of our mentality", and not a blame on Socialism or the government. Other kind of people would say "if Stalin were alive, we would now live better, it was Khrushchev and the others who messed up the things".
Moreover, Capitalism was considered simply morally wrong, even if efficient. So even if you would succeed to convince a person that Capitalism is more efficient than Socialism, a common reply would be "Well, maybe, but it is unjust and immoral". Imagine you would try to convince somebody in the USA that a dictatorship like in Saudi Arabia is more efficient and people there live better. Most likely a common person would reply "Okay, but it is unjust and immoral".
Now, about the dissolution of the USSR. While in ethnic republics there could be politicians who advocated the secession or dissolution of the USSR, in Moscow not a single politician could advocate it because it would be a political suicide.
Even Yeltsin later claimed he was not for the dissolution of the USSR, but that the USSR could not be saved.
Even the far-right Monarchist Neo-Nazi group "Memory" were against the dissolution of the USSR, rather calling it a Judeo-Masonic conspiracy.
The same goes for the Zhirinovsky's Liberal-Democratic party, and quite every other political group.