These performances don’t necessarily offer an exact road map for 2014’s Democrats. Ms. McCaskill was generally considered an underdog until Missouri Republicans nominated Todd Akin, whose candidacy crumbled after his infamous “legitimate rape” comments. If Ms. McCaskill had been defeated by a stronger challenger, as most analysts thought was likely, that would have been a strong precedent for Republican candidates in 2014: Missouri is a more competitive state than Louisiana or Arkansas.

Mr. Manchin’s strength in West Virginia would also be difficult to replicate elsewhere. He was a popular governor who became a senator in 2011, and was therefore unusually well positioned to run against the Obama administration. He famously took “dead aim” at the proposed cap-and-trade bill on carbon emissions by shooting a copy of the legislation in a political advertisement.

Mr. Nelson’s performance in Florida in 2012, though, should be encouraging for today’s Democrats. Mr. Nelson was first elected in 2000, around the same time as Ms. Landrieu and Mr. Pryor. Running for his third term, he had the disadvantage of having voted for the Affordable Care Act. He began the campaign with mediocre approval ratings. He was a Republican target, and early polls often showed a close race.

Yet Mr. Nelson won re-election by a 12-point margin. Most important, although he did not carry the conservative Florida Panhandle, he ran far ahead of Mr. Obama there. It is a region of the Deep South full of voters similar to those that Democrats will need to win Louisiana or Arkansas.

Mr. Nelson routinely outperformed Mr. Obama by a net 30 points in rural areas of the Panhandle, and even won Liberty County, where Mr. Obama received just 29 percent of the vote.

Over all, Mr. Nelson lost the Florida Panhandle by a 9-point margin, overperforming Mr. Obama by a net 16 points in the region. Mr. Nelson’s showing was even slightly better than Bill Clinton’s in 1996, a year when Mr. Clinton won a majority of the vote in both Louisiana and Arkansas. If Mr. Pryor in Arkansas and Ms. Landrieu in Louisiana can also win back the voters who have abandoned Democrats since the Clinton years, they’ll be well positioned.

But Mr. Nelson was not immune to growing polarization in the South; his performance in the Panhandle was the worst of his Senate career. If Mr. Pryor and Ms. Landrieu also have the worst performances of their career, they’ll probably lose re-election: Neither has won more than 53 percent of the vote in a contested race. Their two states are solidly Republican: Even a net-16-point improvement over Mr. Obama’s performance, like Mr. Nelson’s in the Florida Panhandle, would fall short in two states where Mr. Romney won by 24- and 17- point margins.