Hillary Clinton has a small lead over Bernie Sanders in Iowa (possibly as small as 10 points). In New Hampshire, Sanders is leading Clinton. Those are the first two caucus/primary states, and if the election was held right now, Clinton would come out of those two elections with a tiny lead over Sanders (maybe even tied).
South Carolina is the third state to pick their delegates, and that is where Clinton is likely to carve out a significant lead over Sanders. Just look at the results of this Public Policy Polling survey done between September 3rd and 6th. They surveyed 302 Democratic primary voters with a margin of error of 5.6 points (and 764 GOP primary voters with a margin of error of 3.6 points).
The poll shows Hillary Clinton (54%) with a 30-point lead over Joe Biden (24%) and an enormous 45-point lead over Bernie Sanders (9%). It seems obvious that Sanders is not doing a good job of selling his candidacy to Southern Democrats. That could change after the first couple of debates, but he has a lot of ground to make up. No other Democrat got more than 2% support.
On the Republican side, Donald Trump leads the pack with 37% support. Carson (21%) is 16 points behind, and Bush and Cruz (tied at 6%) are 31 points behind. All the other GOP candidates got 4% or less. The Republican race has been pretty volatile and could easily change again, but right now it's a two-man race in South Carolina (and nationally).
