>Do you think we could wipe out all furry mammals, for example?

lets go with over a particular size. Lets say larger than the biggest rat. In that case yes, very easily. Once you get to rats it becomes far more difficult and you're pretty much just destroying the biosphere at that point.

> It assumes that intelligence basically can overcome any obstacles

In the case of human extinction, no, a super intelligence would not have to overcome any obstacles, it would just have to overcome obstacles better than we did.