Clinton was running far ahead of Dole in September and October. I remember he had a 10 point lead in Georgia in October 1996 and he was in range in states like Alabama, Mississippi, and Texas (and of course, he won Louisiana and Arkansas by big margins)--hard to believe today.
Dole made somewhat of a comeback by late October. The DNC financing controversy regarding China helped him somewhat. Plus, his 96 hour nonstop run at the end of the campaign brought him a lot of goodwill and brought the base out to vote. And the Republican vote was more out in force than usual to hold the majority in the House and Senate.
Certainly. However, I remember reading a quote one time from a campaign adviser or something that said Clinton was really mad he didn't flip the entire South. He was set on being that Democrat that brought the South back into the fold (while also making other gains elsewhere and therefore winning in a landslide), and I remember reading that it actually bothered him a lot that he couldn't get a Carter 1976-type sweep (i.e., possibly excluding Virginia and with Texas and Oklahoma a stretch). A lot of people forget that this was still during (or at the latest shortly after) a time period where a lot of political scientists believed that any Democrat winning nationally had to have a very good showing in the South and likely a Southerner on the ticket. It wasn't until post-Bush 2000 (I'd argue) that Democrats felt they weren't reliant on at least a large portion of the South, and even looking back at some posts on this site from circa 2004 that I've stumbled across, people never thought of the South as non-competitive until after Bush won in 2004. The region tended to have wild swings (see 1972 to 1976, LOL), so it appeared "solid" for whomever won it, and today it's very easy to spin a tail of "South became GOP after Civil Rights Act except Carter who was Southern and then Reagan sealed the deal in 1980 by appealing to racists better than Ford," but most contemporary texts in the 1960s, 1970s and 1980s that I have run across place the South as a battleground region, and I believe it was thought of that way even into 1996 by many.