Barbour called the debt-limit showdown Republicans' "point of maximum leverage," and he said he wouldn't like to see the House GOP authorize an increase in the debt limit without an ironclad agreement in place beforehand to address spending in both the short and long term.
Barbour made the comments as he heads to South Carolina for a two-day swing, which includes stops in Charleston, Lexington and Columbia to attend county GOP conventions.
He made his first trip to New Hampshire on Thursday, where he visited a gun store, a French-Canadian diner and spoke to Republican primary voters.
"Barbour is an old French name,” the two-term governor remarked to Manchester Mayor Ted Gatsas.
—Peter Schroeder and Erik Wasson contributed.