"[In] the end, it's a fight they can't sustain," Gingrich, who unsuccessfully sought the GOP presidential nomination last year, said Tuesday on CBS' "Good Morning."
"No one is going to default," the Georgia Republican said. "No one is going to allow the United States to not pay its bills. No one is going to accept the economic costs. It rallies the entire business community to the president's side."
Gingrich said congressional Republicans have two better arenas in which to make their stand: the continuing resolution funding government that expires in March, and the sequester, which automatically cuts spending across the board unless it's addressed.
"[Those] two fronts they can fight, and they have much less resistance from the average American and it's much harder for the president to oppose them," Gingrich said.
Outgoing Treasury Secretary Timothy Geithner said in early January Congress must increase the debt limit within the next 10 weeks after Washington reached its authorized borrowing limit of about $16.4 trillion Dec. 31.