But the Republican path gets much steeper if they lose any of the three vulnerable seats they already hold. In two of them, Georgia and Kentucky, Republican primaries have eliminated tea-party challengers that GOP strategists believe might have helped Democrats to unexpected wins—as occurred in five different Senate races in the 2010 and 2012 elections. Mississippi is the one 2014 primary contest left with the potential to do that again
That risk has grown in recent weeks due to a bizarre incident roiling the Mississippi fight. Supporters of McDaniel entered a nursing home, snapped photos of Cochran's wife, who suffers from dementia, and posted them online.
Read More Time for Democrats to panic over economy?
The incident triggered felony charges—and attack ads from both sides. "Had enough?" asked a Cochran spot. McDaniel has countered by saying neither he nor his campaign was involved, and accused Cochran of smearing him.
Though the incident may have disgusted voters, it has not dramatically undercut McDaniel's support. Polls show the two candidates running nearly even. Intra-party battles are often unpredictable, given their relatively low turnout. About 300,000 voters are expected to decide the race.
Read MoreObama's data gurus take on new lives
Beyond their differences in age, the two candidates represent a portrait in stylistic contrast. The genial Cochran, in line to become chairman of the Appropriations Committee if Republicans regain control, has consistently brought home federal dollars to Mississippi, the poorest state in the union. The more acerbic McDaniel accuses him of excessive cooperation and willingness to tolerate big spending.
—By CNBC's John Harwood