The person making this original statement probably meant it to be somewhat witty and a tongue in cheek barb thrown at either a politician of their day or someone in the wood handling business.
With so much political correctness running amuck, I'm surprised that some wild-eyed, but purported to be well meaning, person hasn't set upon this statement and created a decree correcting it to their liking.
So what could anyone possibly find wrong with this somewhat ancient statement? Following the normal rationale of those that think the government can and should fix everything I offer the following.
1- The "How much . . " tells me that an effort is being made to establish wood chucking standards before determining whether or not it's even possible for this rodent to chuck (toss) the object in question.
2- How much "wood . ." this critter may not even want to chuck wood at all, preferring small pebbles instead, so why can't he/she have the freedom to chuck whatever object they desire?. . this is America after all!
3- How much wood "could . ." seems to be striving to reach the uppermost physical limits of this furry creature's chucking abilities. What if it's having a bad day or gets a blister on it's little paw - - would it receive marmot demerits for not achieving it's maximum capabilities?
4- . . "a woodchuck chuck . ." a chuck or toss to one species might appear to be a clumsy drop to another - - is this comparison fair?
5- . . . "if a woodchuck . ." this "if" is a racial slur to the whole marmot species in general and the woodchuck in particular. It implies that this whole race of animals is inept and incapable of anything more than simple burrow digging.
6- . ."could chuck wood." - - this "could" should be changed to "would" - giving some choice as to whether or not each animal would desire to be made a spectacle of just to entertain someone by their abilities.
It is fortunate indeed that the gender of the animal isn't mentioned as this would possibly bring forth a whole new set of questions.
As you see this old statement places a lot of mental and emotional pressure on the woodchuck - no wonder it spends a lot of time underground - - probably has split ends on it's little fur. ec