Here's my thoughts on this:
Putin has always had a very high approval rating in Russia, sometimes artificially so due to the state control of the press. Whenever there has been a government fuckup, Putin sacrifices a close minister, that person takes the fall, and Putin is seen as a strict ruler - which Russians like. They cheered, for instance, when the Putin gov't imprisoned Mikhail Khodorkovsky for tax evasion for 20 years and broke up Yukos. European football fans will be familiar with the arrival of one Roman Abramovich into European football's ownership in 2003 - Abramovich was essentially exiled by Putin.
The Pussy Riot case shores up Putin's approval with the religious and with men, but it will cost him a lot of female support - an area where he was always having high approval rates. Garry Kasparov, I am glad to hear, is present at the case (if beaten) - he is a high profile Russian that just can't disappear, as many have under the Putin regime, and has been a centrepiece of political action before. In the end, though, it's going to be difficult for any political action to break the alliance between the ROC and the Putin government. 63% of Russians are Orthodox, most actually worship as there is little social stigma to not being a member of the Church - and most importantly, those 63% are ethnic Russians living in Russia. They are the concentration of wealth and political power. Anyone who has money/power and isn't Orthodox is either non-denominational Christian or an atheist. It's going to be tough to break that alliance.
In addition, internal Russian media will not hover on the Pussy Riot case. By tomorrow, it'll be gone from the state media, and before long, from the other major news outlets. There is little freedom of the press in Russia. We'll watch from the outside, but it will take repeated actions of similarly brave people for this style of freedom of speech to become accepted. It makes me very, very happy I live where I live.