What’s the fallacy in this argument?

It's basically a Strawman/selective argument that distorts the anecdotal tale of a young girl whose Grandfather taught her to shoot BB guns in the backyard but then distorts it (non sequitur) to a remark Obama made about an American class of voters who cleave to their guns and god. It then, (again, non-sequitur) assigns this to the comments of a presidential candidate in order to 'poison the well'. 

it's blatant political rhetoric and deceptive, but on the level of propaganda and not logical fallacy.

I can't see that it is an argument at all. Grandpa is merely expressing his opinion (even if it is wrapped in an obvious ad hominem (guilt by association).

The "He was obviously the person Barrack Obama had in mind..." part is amazing familiarity fallacy (nobody can "obviously" know what another one has in his mind).  Also, the use of the word "obviously" is alleged certainty.

The "gun owners" which became "gun owners and other rural people" which is said to include "the little girl with her grandpa and the BB gun" is an obvious strawman fallacy (I don't think Obama meant BB gun owners as "gun owners" or "other rural people" as clingers). 

Using the fond memory of a little girl with her grandparent shooting food cans (which as an act is a pretty innocent usage of BB guns) to divert from not-so-innocent use of real guns is both a cherry picking and appeal to emotion because it is implied that Barrack Obama ultimately what he tried to do is mock a little girl and her grandparent for living happily and creating memories, so the part that is implied is "who would support such a horrible person?",

Which leads to the final part the "elitist Harvard trained community organiser" which is argument by emotive language (the use of "elitist" has generally a negative conotation, as well as the word "safari"). The juxtaposition of "Harvard trained" vs the "small town folks" is the Juxtaposition Fallacy implying that they are on a "safari" BECAUSE they are Harvard trained against the others who are simple, uneducated people. Which is also a genetic fallacy since the truth of the argument about gun ownership depends on whether the person making it is an elitist Harvard trained community organizer or not.

And since this is a response to Obama's opinion without attacking the actual argument but instead attacking Obama for being a "Harvard trained community organizer" it's an ad hominem (guilt by association).