Portman does little to bridge the significant gender gap among Ohio voters. Adding Portman to the ticket marginally improves the Republican standing among men, from 50-40 percent to 51-40 percent, and among women from 49-38 percent to 49-41 percent.

Remarkably, nearly six in 10 Ohio voters say they don't know enough about Portman — who won election to the Senate in 2010 — to have an opinion of him. Of those in the state with a formed position on their senator, 26 percent view him favorably and 14 percent unfavorably.

Romney, President Obama and Vice President Biden all see virtually even splits in their favorable and unfavorable polling in the states, underscoring the true swing nature of Ohio. Republicans have never won the White House without securing the Buckeye State.