what does stick to my teeth mean?
and dig in?
We have "stick to your ribs" and "skin of your teeth" but "stick to your teeth" leaves me cold. I think it was garbled in transmission to you.
"Dig in" is derived from military tactics: soldiers dig holes to evade enemy fire and to make rough fortification against attack. These holes are "foxholes" -- more elaborate ones could become "trenches" as in WWI. The trench becomes more or less a permanent fortification; the foxhole is a make-shift temporary measure (so the soldier hopes, anyway).
So, to "dig in" means, to take a position and fortify it against attack. It is used metaphorically... as in...
The more we argued against her Creationist views, the more deeply she dug in.
Or, it is often used literally in a military context:
The Allied shelling of Normandy failed to dislodge the Germans, who were considerably more deeply dug in than Allied intelligence had reported.
Tangent A: Slang -- "There are no atheists in foxholes."