Americans have an inborn distrust of government that goes back to the American Revolution. at its best, this instinct gives us a cynicism that causes us to question whether the government is acting on our behalf as a people, or on behalf of vested special interests and/or power-hungry individuals in elected office.
However, there are a large number of individuals who are convinced that a near-complete absence of government is desirable. These people are fully confident in the ability of business to regulate itself. These are the people who think that global warming is a world-wide liberal environmentalist plot. These are also people who, while calling for elimination of government regulation of the Savings and Loan and the Banking Industry, watched these industries milk the system and blamed their misbehavior on poor people who shouldn't have gotten loans in the first place.
These people will tell you that Gridlock- no government action at all-is preferrable. Some of the Tea Party folks were elected on just such a platform.
I think this concept is extremely difficult for Europeans to grasp. What lies at the basis of it is scepticism about ANY information which is disseminated by ANYONE, since all media are thought to be controlled by pro-government forces. These people are inclined to trust only information which supports their existing belief system, which means that the majority of their input comes from demagogues who feed them opinion based primarily on anecdotal evidence, since no real studies can be trusted (read talk radio and FOX tv pundits).

So to answer the question, yes, it will have an impact on Obama, since gridlock will become the ruling legislative paradigm, and I see no further legislation of any substance being made law. Instead of a forum for change, congress is likely to become a platform for posturing.