"What happened was non-essential government services were temporarily suspended. That happens every single week on the weekend. The world doesn't end."
Tea Party-backed lawmakers are hoping to rally support for a government shutdown threat until Obama agrees to cut all funding for healthcare reform, which would essentially nullify the law.
Establishment Republicans have come out strongly against the plan, saying it would prove fatal to the GOP.
Cruz acknowledged that a shutdown is not a "sustainable long-term situation," but said it would not be "as calamitous as many paint it."
"The received wisdom that  was a disaster I think is completely wrong," he said.