Robert L. Woodson Sr. is a no-nonsense black conservative who heads the Center for Neighborhood Enterprise and knows a thing or two about that culture, the nation’s inner cities and Mr. Ryan.

“Paul approached me about a year ago,” says Mr. Woodson, sitting recently in his Washington office. “He knows we have groups all across the country that deal with the plight of the poor. He asked me to take him on a listening tour. He said, ‘I’d like to learn about the alternatives to what we’re already doing, and I know you’ve been involved in assisting people at the local level.’ ”

Mr. Woodson agreed but warned that there would be a time commitment. “I said to his staff, ‘I don’t do drive-bys, so he’s got to give me an entire day.’ If you’re serious, you’ll put in the time. And he did. I’ve taken him now on 12 trips—all to high-crime, drug-infested neighborhoods. And he was not just touched but blown away by what he saw.”

Mr. Woodson believes that the Ryan brouhaha could turn out to be a blessing. “Low-income people haven’t been on President Obama’s agenda for five years,” he says. If this sparks a conversation, all the better, “but we have to have the right conversation.”