I'm sure the FSB has the likes of Naryshin, Patrushev or Bortnikov up their sleeve with Putin out of the picture. Putin was virtually unknown when he was first appoined as president. Win a Chechen war by throwing countless human and material resources at it, then you're wildly popular. If you come to think about it, Russia has only gained territories during Putin's leadership.
The political landscape in Russia is basically this: United Russia, commies and ultranationalists. All of these are pro war with the exception of a single party with a single member in the Duma, which opposes the war due to economic reasons.
