Let's start with your second question: is it correct to blame slavery on democrats and liberals?

No, certainly not. There were a lot of factors, and perhaps if you came to a satisfactory definition of "democrats" or "liberals" you could show that they somehow contributed. But assigning "blame" - that's a hairy operation for a whole lot of reasons. I won't go into it, but basically: this is empty rhetoric.

Your first question is a good one though, and I'd like to try to help explain the current "solid republican" shift in the South. Check out these two electoral maps:

http://upload.wikimedia.org/wikipedia/commons/5/55/PresidentialCounty1956.png

http://upload.wikimedia.org/wikipedia/commons/7/71/1964prescountymap2.PNG

These are from two presidential elections - 1956 and 1964 - and while they are not perfect representations, I think these two maps get at the heart of the question you're asking: how did this happen?

I can't give you a full answer here - this is a broad topic with many factors involved - but certainly the civil rights movement played a part. And the other big one would have to be the the whole "Southern Strategy." Essentially, the Republican party decided to make the south vote for them through policies tailored to the demographics, and they succeeded.

Here's a more in-depth treatment of the Southern Strategy:

http://www.reddit.com/r/AskHistorians/comments/1jf84n/what_is_the_realty_about_nixons_southern_strategy/cbe8vvs

That's much better than anything I could provide before lunch, so check that out and you should find further reading if you want to keep investigating.

Good luck!