Julian E. Zelizer is a professor of history and public affairs at Princeton, and the author of “Jimmy Carter” and the coming book “Governing America.”

“I’D rather be a really good one-term president than a mediocre two-term president,” President Obama confessed to ABC News’ Diane Sawyer last year. Other than the “really good” part, Republicans would be happy to see this wish fulfilled.

With waning approval ratings and a stagnant economy, the possibility that Mr. Obama will not be re-elected has entered the political bloodstream. Suddenly, the opposition party envisions a scenario in which its presidential candidate could defeat Mr. Obama in a referendum on his job performance. Mr. Obama needs to think hard about his own statement and consider what it takes to be a successful one-term president, in the light of history.

One-term presidents usually leave office with their parties divided, the economy in crisis, wars unresolved, approval ratings in the tank and a sullen public rejecting them. Becoming a one-term president means joining a gallery of dashed hopes and crushed ambitions. Among those who were elected for just one term were men who, like Mr. Obama, came to the White House with enormous promise....

IF 2012 is really the end of the road for President Obama, it is possible to see how historians might look favorably on his term. The president has already accomplished a great deal. His health care reform legislation promises to expand health insurance to millions of people and correct a number of flaws in our current system. His economic stimulus helped to stave off a second Depression and preserve the auto industry, while his financial regulations are meant to curb some of the abuses that led to the financial collapse of 2008. He has used executive power to strengthen some environmental regulations, while on foreign policy the killing of Osama bin Laden constituted an important step in the war on terrorism. Most recently, the role of the United States in the collapse of the rule of Muammar el-Qaddafi in Libya marks another victory in the struggle against dictatorships....

Since the 2010 midterm elections, Mr. Obama has governed from such a defensive position that he risks undercutting those gains. The president has to make sure that his embrace of deficit reduction through spending cuts does not jeopardize his health care reform. He must also make politically difficult choices, like following through on his promise to push for an end to the Bush tax cuts for the wealthy, even if his close advisers fear that such a stand will blow up in their faces come Election Day. The president’s speech on jobs was a start, but the follow-through is critical....