As always, it's important to remember that reducing the projected federal deficit, as the CBO estimates that House Speaker John Boehner's deficit plan would do, doesn't always mean spending less. It's easy to call these projected deficit decreases cuts (I've probably done it myself), but they're not really true spending cuts in the way that most people think of them.
Even when there are no new taxes, reducing the deficit typically means reducing it against the projected baseline—a projected spending schedule under which total spending is expected to rise. So as Cato's Chris Edwards explains, "the Boehner plan doesn’t actually cut spending at all." Edwards goes on to illustrate how discretionary spending, the portion of the budget which Congress has the most year-to-year control over, would rise each year under the Boehner plan, increasing from a projected $1.043 trillion in 2012 up to $1.234 trillion a decade later.
Neither the Boehner plan nor the Reid plan, if enacted, would reduce spending from today's levels. Instead, they'd merely slow the rise of federal spending. That's better than allowing it to continue as planned. But it's far less than the sort of fundamental reform our current dismal debt trajectory requires.