"It's irresponsible of the president and his men to even talk about default," Paul said during an appearance on NBC's "Meet The Press." "There is no reason for us to default."
The federal government is set to hit its borrowing authority on October 17, according to the Treasury Department.
Paul said the government can avoid default by paying its interest beyond the debt ceiling deadline, and accused Obama of using threats to scare the public.
"This is a game," Paul said. "This is kind of like closing the World War II memorial. They all get out on TV and show we're going to default, they're the ones scaring the marketplace."
Earlier Sunday, Treasury Secretary Jack Lew appeared on several Sunday talk shows to warn of the potential dangers to the economy posed by breaching the debt limit, accusing Republicans of "playing with fire" by refusing to raise the debt ceiling.
"There is no option preventing us from being in default if we don't have the cash to pay our bills," Lew said during an appearance on CNN's "State of the Union."
House Speaker John Boehner (R-Ohio) also warned of a potential default on Sunday, pinning blame on the president's refusal to negotiate with congressional Republicans.
"That's the path we're on," Boehner said on ABC's "This Week." "I'm willing to sit down with the president, but his refusal to negotiate is putting our country at risk."