Hard to say. It depends on the details.
When you lose the SEC by a 4th Qtr pick 6 to the eventual national champions, that's close enough to taste it.
Hypothetically, if we, go 11-1, losing only to an undefeated UF team who wins the NC this fall (and thus we don't even win the east--thereby avoiding all the piss on the east posts here), it would take utter stupidity to fire Fulmer.
Who on the face of the planet worth their salt would take a job at an institution that clueless about the realities of winning championships?
My ealier prediction for this fall was that we'd go 11-1 in the regular season, losing only to Auburn, who we beat in the SEC CG, but then don't get to go to the NC because of an undefeated Big 10 or Big 12 champion playing USC. There's no way any objective person would want to fire Fulmer under that scenario.
If the Vols win 10 or more games (as they did last year), and don't win the SEC championship, my guess is that Fulmer will stay as long as he wants. Such seasons in the SEC are far from a being a cake walk for any coach.
Lombardi would not dominate the SEC as it is now. No one will.