You are absolutely right. If Putin backs off, he will lose a massive amount of support from the Russian people. Expect to see big demonstrations in the street.
By the way, did you know that official rumour has it that Putin will have himself installed as president of Gazprom when his 2nd (and last) term is over? Kind of reminds you of that "market economy" called Germany - with Schroeder taking the plum job after leaving goverment - doesn't it?
We in Russia see what a "genuine market economy" does for USA - with Katrina response, tax cuts for poor, etc. - and we don't want it!!!
I am not sure that the type of economy determines how the government responds to emergencies. Did the Soviet government do any better after Chernobyl disaster than the U.S. administration after hurricane Katrina?