The Daily Beast says it can happen, but most of the time debates don't make much difference, because most voters have already decided who they are going to support in November.
A 2008 Gallup study found that between 1960 and 2004, there were only two years where debates made a difference in actual votes. Instead, the most common outcome of the presidential debates is a slight popularity bump. But that bump doesn't necessarily translate into votes.
"They sometimes have a short-term effect, a bounce in response to the debates, but at the end of the day there often is not much of an effect," says Robert Erikson, author of The Timeline of Presidential Elections.
Data from the Gallup study also saw no direct correlation between the winner of each debate and the winner of the presidency. The 2004 Kerry vs. Bush debate was cited as an example. Kerry was considered the victor of all three showdowns, but still lost the election.