Barack Obama became president under an unusual set of circumstances. Most presidents can expect to be praised or blamed based on what happens during their administrations: if the economy is good, they will get the credit (or at least will benefit from the good feeling in the electorate), and if it is bad, they will be blamed. One exception to this was FDR, who inherited a disastrous economy. Everyone blamed Hoover, and it didn't matter that FDR didn't do much to bring about recovery; he got a pass because the economy was a disaster when he took over.
Obama is in a similar situation on the economy. Thankfully, things are not nearly as bad as the Depression (despite what some people say), but they are worse than they have been in a long time. Because this started six months ago, while Bush was still president, he gets the blame. No one expect Obama to turn the economy around instantly. I expect that he will not start attrating much blame until the end of 2010, if the economy is still bad by then. Most economists predict the recession will last that long, so we may get a chance to see whether this is true or not.
On the other hand, the situation in foreign policy is nearly the reverse. People have widely criticized Bush's foreign policy, especially the Iraq war, but there is no denying that the United States has avoided a terrorist attack since 9/11. Since Obama has so roundly denounced Bush's approach to terrorism -- even changing the name of the "war on terror" -- he will be in big trouble if the terrorists strike again during his first term. (Maybe his second, too, if there is one, but that's too far for me to predict.) Just as it doesn't matter why the economy actually tanked last year, it doesn't matter why there have been no terrorist attacks on U.S. soil since 2001, and it won't matter much why one happens in the future: Obama, and his new policies, are going to take the blame. The same goes, to a lesser extent, for Iraq. If Obama pulls out of Iraq quickly as he promised, the Iraqi government could collapse, become a revolutionary Shi'a state, and/or become a new haven for terrorists. Any of those things would make the withdrawal appear very shortsighted. (However, based on what happened in South Vietnam, I'm not sure how much this would affect his popularity outside of professional journalists and politicians; Iraq is a long way away.)