Edwards said Thursday that events like the one where he spoke - which drew several multiples of Columbus' population of 229 - showed untapped support for his platform of paying attention to rural America.
The former North Carolina senator blamed pundits for giving too much weight to campaign contribution totals inflated by money from lobbyists that he refuses to take.
"They think that when you come to communities like this, it doesn't matter," he said. "The only thing that matters is fundraising contests, who can raise the most money, who can get the most money from special interests."
Edwards said he would rely on a grass-roots and Internet-based campaign to build support among rural voters and others not traditionally targeted by campaigns.
"Electability goes way beyond money," he said. "My campaign will not be limited to New York and Los Angeles and Chicago."
He told listeners their votes could decide "we're not going to replace a crowd of corporate Republicans with a crowd of corporate Democrats."
In fundraising figures released by some candidates this week, Edwards reported raising $7 million for the summer quarter, far behind the $27 million generated by New York Sen.and the $20 million reported by Illinois Sen. .
Edwards has said he plans to accept public financing that could boost his overall fundraising by about $10 million. He reported having $12 million cash on hand.
Edwards spoke at Columbus-Belmont State Park, which was built in 1934 by the Civilian Conservation Corps - part of President Franklin D. Roosevelt's New Deal program for fighting the depression.
The park is on the site of a Confederate stronghold known as the "Gibraltar of the West" that was defended by 140 cannons and used a heavy chain to block Mississippi River traffic.
He made an eight-state tour this summer of inner cities and several rural communities across Appalachia and the South to highlight the issues of America's poor.