Race has definitely affected Obama's presidency. It is very evident that people hold him to much stricter standards than they would for past presidents. People also have a tendency to call him racist names and make assertions about his religion and place of birth that have no basis in reality. White presidents have never had to defend their birth certificate in such a way.
Times are obviously much more different then they were long ago. I feel at this point, the majority of Americans were not too worried about President Obama's "race", and more concerned about his general performance as our President, and what he can bring to the table, as far as improving the country.