Err... really? Sixty million American Bison disappeared from the Great Plains because they were big? Then why did the passenger pigeon over the same period go from the most numerous bird in the world to extinct? It's true that the largest baleen whale -- the Blue Whale, is listed as "threatened"; but the smallest baleen whale, the pygmy right whale is either extinct or very close to it.
It's not as simple as big == headed for extinction. Sometimes bigness is a factor in extinction, sometimes it's a factor in survival.