A recurring theme in the debates and discussions about the debt ceiling is the notion that the Republicans want any increase to be matched by an equally-sized spending cut. If your political persuasion says that increasing the debt ceiling is bad and cutting spending is good, then this may sound like a good balance---a fair trade, one-for-one.
However, it's basically a stunt. When they talk about the size of a spending cut, it's generally in terms of how much is spent over a ten-year window. That is, raise the debt ceiling a trillion dollars, reduce spending by a trillion dollars over the next ten years. The problem, as any physicist can tell you, is that these two quantities are incomparable because they have different dimension. They aren't expressed in the same units. One is in dollars; the other is in dollars per decade. Equating them is like asking your friend, "how far is it to Austin?" and getting the answer, "seventy-five miles per hour".
The problem with this stunt is that it's completely arbitrary, because the window of time is arbitrary. Sure, ten years is a nice round number, but that's your first clue that it has no actual significance or relevance to the situation. Furthermore, increasing the debt ceiling and cutting spending don't really balance each other---in fact, they work together to delay the next time we risk hitting the debt limit. (To the first order, that is---I won't attempt to work out the higher-order effects of changes in spending.)
So, there's no reason to think that the ideal mix between these two actions is the one that decreases the ten-year spend rate by an amount that is numerically equal to the one-time debt ceiling increase. They're really two separate things that should be considered separately. So when someone talks about the two needing to be equal like it's a law of nature or something, know that they're trying to fool you and make their argument sound better than it really is.