This is not the first time that Vladimir Putin has been forced to respond to a Russian tragedy. Ten years ago this week, he confronted the sinking of the submarine Kursk, with the deaths of all 118 on board, by first denying that there was a problem, and then refusing assistance from the US and Britain until it was too late. Those who criticised his handling of the disaster were silenced, including families of the deceased.

But Putin is best known to Russians as a strong leader, a "man on horseback" in the tradition of Stalin and Peter the Great. Putin's presidency began with the second Chechen war, a campaign to eradicate Islamist separatists and terrorists accused of bombings in Moscow and other cities. Putin's popularity crested with his image as the kind of strong leader who could play tough – even dirty – when the circumstances merit.

Now, as Prime Minister, he is rolling up his sleeves to take charge and is once again the man on horseback. Although fire-fighting efforts have been woefully inadequate, Putin's personal popularity will swell, at least in the short term.

For Medvedev, the short-term prospects are less bright. He has been a very different kind of President. With Putin positioned protectively close, he plays the role of diplomat-in-chief and apostle of Russia's "modernisation" drive, which entails forging closer ties with the West and fighting corruption. But to average Russians, the suave young President appears no match for the challenge of this firestorm.

In the longer term, however, it may be Medvedev that benefits more. Citizens are asking how Putin's power structure could have allowed so much local corruption and ill-preparedness, and complaining that even Soviet-era leaders were more effective.

With presidential elections still two years off, there is plenty of time for new crises to remind Russians why Putin's toughness might still be needed. Medvedev himself has said he will step aside if his mentor decides to run. For now, just like the smoke-blotted Moscow skyline, there is little daylight visible in Russia's "tandem" leadership.

Matthew Rojansky is deputy director of the Russia and Eurasia programme at the Carnegie Endowment for International Peace