THERE IS ONE overriding task for President Obama and the Democrats at the convention in Charlotte this week: to give substance to the vision of a second Obama term. The president accomplished more in his first term than Republicans in Tampa last week gave him credit for. But he also has disappointed in ways that we, like many voters, hope a second term could overcome.

Embedded in this convention mission are numerous tasks. One is defending the achievements of the first term. Despite the difficulty of answering the are-you-better-off question in the midst of a sluggish recovery, Mr. Obama needs to explain how his actions eased the economic crisis and took on long-standing challenges such as extending health-care coverage to millions of uninsured Americans.

At the same time, Mr. Obama must explain why he was unable to fulfill his promise to overcome the “broken politics in Washington.” Many Republicans were determined from the start to derail his agenda and prevent his reelection. Yet an implacable opposition is hardly the whole story. At key moments of his presidency, Mr. Obama ducked the duty to lead in forging bipartisan solutions to the nation’s biggest problems. Seeking reelection, he needs to explain to voters fed up with Washington gridlock and bickering why they should expect the next four years to be different from the last, and why they should be confident he will step up to the task.

As we said last week, Mr. Romney’s acceptance speech was disappointingly light on agenda. Mr. Obama similarly should explain where he would take the country if given a second term. So far, he has been better at criticizing Republicans for wanting a return to what he describes as the failed policies of George W. Bush — a trickle-down, rerun agenda “better suited for the last century,” he said over the weekend — than in framing his own.

Specifically, what would Mr. Obama do to restrain health-care costs and entitlement spending? How would he reduce the national debt to a sustainable level, where would he find revenue beyond taxing the rich, and can he enlist at least some Republican help in either goal? How would he ensure that the war in Afghanistan ends in a way that protects U.S. security interests as well as basic human rights in that country, and how will he prevent Iran from obtaining a nuclear weapon? Would he, in a second term, adhere to the concern for endangered civilians and the promotion of freedom he boasted of in Libya or to the hands-off policy he has followed in Syria?

Mr. Obama rightly promises to rebuild the nation’s economy and bolster its middle class by investing in education, science and infrastructure. But that will be an empty promise if the nation cannot get a handle on its long-term finances.

Republicans in Tampa, Mr. Obama said, offered “a lot of talk about ‘hard truths’ and ‘bold choices,’ but the interesting thing was nobody ever bothered to tell us what they were.” Fair enough. We hope he will do better.