PHILADELPHIA — Follow along with our coverage of the Democratic National Convention.

This is not about me, President Obama kept telling his closest advisers in recent weeks as he labored over one of the last major addresses of his presidency.

But he could not avoid the subject. And as he took the stage here Wednesday night to rally Democrats around Hillary Clinton, Mr. Obama’s diagnosis of the nation’s current political failings inevitably called to mind the promise of reconciliation and unity that propelled his improbable rise, but that seems even more out of reach today.

“We get frustrated with political gridlock and worry about racial divisions; we are shocked and saddened by the madness of Orlando or Nice,” Mr. Obama said. But he added, “What I have also seen, more than anything, is what is right with America.”