While Kevin Spacey gets some of the accent right, he sounds less like people actually do in the south these days. Here's Vox on that:
There are a couple of distinct features that make Underwood "sound" Southern to some people. One of these traits is his "R-lessness," which an expert would call his "non-rhoticity." "This is when r at the ends of syllables is pronounced like a vowel or deleted, so that car and cars sound like cah and cahs," Becker explained to me. You can hear it in the way Underwood says words like "uninformed" and "careless."
This is one of the features that Thomas considers a stereotypical Southern feature. It sounds the way people think Southerners sound, but it's actually a feature that is disappearing in Southern speech. "R-lessness was a traditional Southern feature — although not everywhere in the South — it was most prevalent in areas where the plantation culture had pre-dominated at one time before the Civil War," Thomas told me, explaining that non-rhoticity had once been considered prestigious.
The post at Vox goes into a little more detail than the video, but one thing is clear, if you're not from the southeastern part of the United States and your characters are supposed to be (and your actors also aren't either), you've got to do more than just drop Rs (or in contrast make them sound super hard). If you can't afford a vocal coach, some of the explanations above can help you get southern accents from non-southern actors sounding far more realistic.
In the end, you've got a better shot at getting a believable accent by really listening to how specific parts of the south form their vowels and consonants, and not just having the actor put on a stereotypical "southern" accent that doesn't really make sense for any part of the region. The best case scenario would be to spend time with people who are from the area your characters are supposed to be, but that's not always an option. IDEA is a great resource if you're looking to hear accents from all over the country (and even the world).