Due to the obvious fact that any amount of debt automatically discredits whoever is presiding over a country, I believe that one the economy collapses indefinitely in Russia, Putin will be threatened out of office and another course of action will have to be insued unless something miraculous happens and this event is prevented.
There is no one else to replace Putin at present. Russian politics are filled with factions and many people expected what has happened. That was the idea of the sanctions to force Russia to raise the rates and lead to a financial collapse. It can seem like bullying Russia into taking action. I'm sure the Russians have a plan though.
Recent polls found that Russian President Vladimir Putin still enjoys an 82% approval rating despite a collapsing economy. This shows the extent to which he is able to control the state media to spin public opinion in his favor. The Russian people are used to hardships and will continue to support Putin to the confusion and consternation of Westerners.
I really don't think that the collapse will push him out of office. What will push him out of office is the way that he reacts to the crisis. If he does well then he will most likely stay, but if he ends up responding poorly and brings the country into an even worse state, he will likly lose his position.