Both phrases use sporting analogies - the first is from boxing - a bare knuckle brawl is a fight without rules or referee, comparable with a street fight where the fighter will do anything to win.
No holds barred is from wrestling and again is a bout in which the wrestlers can do pretty much anything they like.
So Obama plans a campaign in which he intends to do anything he needs to do to win.
Buggles(not a teacher)
Interested in Language