RALEIGH, N.C. — Dexter Hady, a black landscaper here, is exactly the kind of Obama supporter who could have slipped through the cracks this year. He recently moved and, not being as excited about the coming election as he was about the 2008 campaign, neglected to update his voter registration.

By chance, a volunteer for the Obama campaign stopped Mr. Hady outside of the Wake County Courthouse here recently and asked him if he was prepared to vote. Mr. Hady said no, and went on to explain: “I can say I was definitely more excited to vote for Obama last time. I guess part of it is that history has already been made.”

For the Obama campaign, it is almost impossible to overstate the importance of winning over people like Mr. Hady again in North Carolina, which has the largest percentage of black voters of any of the swing states — especially after President Obama’s performance in the first debate, which was widely seen as lackluster. In 2008, a strong black turnout that voted almost exclusively for Mr. Obama was credited with helping to win North Carolina for the Democrats for the first time in decades, contributing to his ultimate victory.

For that to happen again, Mr. Obama would need a near repeat of black voter behavior in Raleigh and across the state. But times have changed. Enthusiasm is down, unemployment is up. And some socially conservative black ministers in North Carolina, where voters passed a referendum against gay marriages and civil unions in May, remain troubled that Mr. Obama endorsed same-sex marriage this year.