First, I don't like the terminology, because it uses the word "negative" to describe rights we hold dear. But to use the terminology, certain "positive" rights do exist. You have the "positive" right to a public trial in the Constitution. On the other hand, such rights can usually be restated the other way, "The government shall not keep the trial proceedings from the public."
This does not equate to, for example, health care. "You have the right to adequate health care" is a socialist type "positive" right. It can't be restated as "the government shall not prevent a person from receiving adequate health care" and still mean the same thing. Public education isn't even a right. It is just something that people from the Founders onwards thought was a good idea.
This is just a generalization though. The issue goes much deeper and could be discussed for months.
You don’t really know what Obama(or any other progressive) thinks about “positive” rights, do you?