Few people view this as a good way to tame the debt.
Yes, keeping the current cap in place would stop all borrowing. But if it caused a financial crisis in the process – as some economists predict – that could end up worsening the nation’s fiscal position. In a recession tax revenues typically go down, and federal spending goes up. By contrast, in the current economic recovery federal spending is falling as a share of GDP, and tax revenues are rising.
Moreover, refusing to raise the debt ceiling would not address the cause of the problem: The programs that are leading to all the deficit spending would still be on the books.