'g-dropping' is associated in American culture with rural or Southern speech, which Texas exemplifies both for most Americans.
But most Americans 'drop' their g's (or really convert ng-final to n-final in present participles) whether Southern, New England, California or anywhere in between, in informal contexts. Newscasters and anyone speaking deliberately will attempt to pronounce it as '-ng' (I don't think this is restricted to the areas so far mentioned).
The g-dropping of people in the news is often remarked upon because it is an easily verifiable marker. I claim that most of the Texan 'feel' comes in the prosody (the 'drawl'), it's just that the g-dropping is something easily verifiable.
Because ng-final is part of the standard dialect/accent, careful speech will attempt to use ng-final. I suspect that Rick Perry/Sarah Palin/Barack Obama/etc are attempting to artificially g-drop for affect (as @ghoppe remarked). g- dropping is part of (most) everyone's daily pronunciation (except possibly newscasters) so it is in fact an effort to not g-drop.
(My data for this is unreferenced, but can be confirmed or denied by listening to the difference between formal (ng-final) and informal (n-final) AmE speech).
As to human character trait, often differences (of any kind) in register or dialect are explained informally by things like provinciality, laziness, stupidity, vulgarity, criminality, deficiencies of formal education in the target dialect, or ... attempting to pander to such audiences. Those reasons are very tendentious and considered scientifically unsupportable, except for possibly the formal education and pandering. Only the latter (pandering) is really considered a negative character trait (and then only sometimes).
There are regional differences of course. In AmE, the general informal accent will do some g-dropping on present participles, and almost always in the 'country-western' accents (Southern US and Midwest). BrE accents will g-drop for some non-present participles like 'anythin' for 'anything' (AmE never does that).
The concept of 'g-dropping' was first made more noticeable by reporters covering Sarah Palin when she was running for vice-president.