Has Mitt Romney committed himself to severe cuts in government spending, undermining programs on which not just poor but also middle class Americans depend? That question has been the subject of debate lately, with smart people like Ross Douthat asserting that Romney's position is less extreme, and less conservative, than liberal critics like me have assumed.

I respectfully disagree. And the single best piece of proof may be a proposal that’s gotten virtually no attention: Romney's proposal to cap federal spending, which would result in harsher cuts to domestic spending than even Paul Ryan has embraced.

How can that be? Start with some budget math. Romney he has vowed that, by 2016, he would cap federal spending at 20 percent of gross domestic product while maintaining defense spending at 4 percent of GDP. That means he would limit all non-defense spending to 16 percent of GDP.

The latest Congressional Budget Office projection suggests that GDP in 2016 will be $19.1 trillion. Sixteen percent of that is about $3.1 trillion. But, based on CBO figures, non-defense spending will be about $3.6 trillion in 2016. So to meet his goals, Romney would have to cut non-defense federal spending in 2016 by roughly $500 billion.

Romney doesn’t deny this. On the contrary, he’s been refreshingly honest on this subject. In the Washington D.C., speech where he laid out his budget vision, he said “we’ll need to find almost $500 billion in savings a year in 2016.” But Romney has not given many details on what that would entail. (Nor did his campaign respond to questions about this from TNR.) Perhaps that's because the impact of these cuts would scare the bejeezus out of some people.