During the 2008 war, Russian forces penetrated into Georgia but didn't threaten Tbilisi or Saakashvili's regime directly, even when it became clear that western powers did little more than bluff. They eventually withdrew on their own accord.
Let's say instead, that Putin is bent on destroying the pro-western Saakashvili. He ignores all attempts to broker a ceasefire and declares a no-fly-zone over Georgia, ordering the destruction of Georgia's air force and navy. Putin isn't dumb enough to order an attack on Tbilisi itself. Instead he orders the Russian army to occupy and/or destroy road and railways, hoping to starve Saakashvili into submission.
According to Putin's hypothetical plan, Saakashvili will go into exile, and most Russian forces will return to Russia. Some will stay behind officially at the invitation of the new transitional puppet Georgian government. Elections for President and Parliament are held, with all pro-western candidates conveniently not on the ballot.
How far could Putin push the war before the west takes concrete action?