In the last 2-1/2 years, annual Federal spending under Obama has been raised by 30% from the $2.9 trillion in Bush's last year in office to the current $3.8 trillion; a near trillion dollar increase in spending. At the same time, revenues have fallen to $2.2 trillion. Even if Congress could roll back spending levels to the pre-Obama, $2.9 trillion, we would still be accumulating debt to the tune of $700 billion a year. Therefore, there is no way to avoid raising the debt limit and I think Republicans should just be straight with the American public and not keep saying that they won't vote to raise the debt ceiling at all.
Of course, it should be made quite clear that if Obama and the Democrats hadn't been so reckless in raising spending, we might not have had to have this debt ceiling debate for at least another 2 years.