Trouble is that without Communism, there's not much in the way of ideological legitmacy to keep the Soviet Union together - the Chinese could use good old nationalism to prop up the regime, which would be dangerous in a state only 50% Russian proper, or fear of chaos and civil war, while for the Soviets the last time they had undergone a Cultural Revolution type fun time had been back during the 30s...
Bruce
I'm not so sure. The Russian Empire in its last decades was based on a mixture Russian nationalism and pure statism, and it wasn't nationalist agitation that brought it down. The Soviet regime is dealing with a literate educated population, but then, Soviet nationalism was much more liberal on questions of language and identity.
And there was such a thing as Soviet identity. People voted for the New Treaty in the Slavic and Central Asian countries and Azerbaijan, and went on to vote for the independence (where they did) of Soviet states based on essentially Soviet identities. Capitalist Ukraine, for instance, celebrates independence day as the day when the Soviet parliament passed the independence declaration, not any of the N other candidates, and commemorates the Great Patriotic War. This was even more pronounced in the 1990s (and would be even more even more pronounced in a Ukraine without the west).
The USSR was a Soviet state, not a Russian one, in the same way that the British state isn't English. So replace Russians with Soviets - a category from which many titular-nationals in the Baltics, Moldova, and so on would exclude themselves, but few in Belarus or Ukraine - and you have a much bigger basis for the state.
(Not to mention that not all of those 49% of non-Russians want independence before even mentioning Belarussians and Dniepr-Ukrainians. What about the Germans, Bashkirs, Kalmyks, Tatars, miscellanious Siberians, and North Caucasians who aren't from Chechnya or Dagestan? They may not be Russkiy, but are Rossiskiy. Small individually, but add 'em up...)