“There’s no doubt that there’s some folks who just really dislike me because they don’t like the idea of a black president,” Obama said
“Now, the flip side of it is there are some black folks and maybe some white folks who really like me and give me the benefit of the doubt precisely because I’m a black president,”
After a president is elected their race or religion diminishes in importance compared their actions. We judge candidates on their beliefs, race, religion, associations, wealth, and political hype because we don't know what kind of president they will be. However, once we elect a president, it's primarily his actions that determine what we think about him.
When JFK ran for president, his religion was a big factor in what people thought about him. After he was elected, it was what he said and did that determined his popularity. Much the same is true with Obama. Of course there will always be people whose judgement is based on the skin color, religion, or ethnicity.
Obama's handling of the economy, healthcare legislation, the war, and his proposals are responsible for most of his positive or negative approval, not his skin color.