Mitt Romney has promised vast reductions in federal spending while also balancing the budget, which would mean a whopping $9.6 trillion in non-defense cuts by 2022. He's largely avoided specifying what he'd actually cut to achieve such fiscal feats. But under questioning from Fortune magazine, Romney provides a few more details.

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"[F]irst, there are programs I would eliminate. Obamacare being one of them but also various subsidy programs -- the Amtrak subsidy, the PBS subsidy, the subsidy for the National Endowment for the Arts, the National Endowment for the Humanities," he told Fortune, according to interview excerpts in Playbook. Romney also wants to "tie the compensation and benefits for federal workers to those which exist in the private sector," claiming that it would save about $47 billion a year.

The problem is, eliminating federal supports for Amtrak and cultural programs would barely save any money. Repealing Obamacare would actually add to the deficit, given the net savings that are in the health-care law. And the savings that Romney projects for tying federal compensation to private-sector levels seem to be overblown, according to recent figures from the Congressional Budget Office. Overall, the cuts that Romney specifies would just be a drop in the bucket, and they still don't explain how his budget would produce the savings that he promises.

Here's how it breaks down: In fiscal year 2012, the federal government spent $1.42 billion on Amtrak, $444 million on PBS, and $146 million on the National Endowment for the Arts and Humanities. Getting rid of all these subsidies would have saved the government about $2 billion this year — chump change relative to the scale of cuts that Romney wants.

Meanwhile, repealing Obamacare would actually increase the deficit in 2013 by $34 billion, according to the Congressional Budget Office, as the law's net savings exceeds  its expenditures. By 2022, full repeal of the health-care law would add $109 billion to the deficit.

Finally, Romney's proposal to tie federal compensation and benefits to private-sector levels would likely produce less than the $47 billion yearly savings that he estimates. Romney is correct that compensation for federal employees is higher than private-sector workers with comparable responsibilities and education: Federal wages are 2 percent higher on average, federal benefits are 48 percent more, and overall compensation (wages and benefits) is 16 percent more, the CBO said in a January 2012 study.

Since the federal government spends about $200 billion a year on compensation for the civilian workforce, according to the CBO, adjusting it to private-sector levels would save about $28 billion annually — significantly less the savings that Romney projects. "Frankly, I can't see that you come anywhere close to that kind of an annual dollar savings," says John Palguta, vice president for policy at the Partnership for Public Service.

Overall, how much of a dent would these cuts make? In 2013, Romney's proposed changes would actually increase the deficit by about $4 billion, because the net savings would be outstripped by the loss in revenue due to repealing Obamacare. In later years, however, more savings would begin to accrue: If continued over a decade, eliminating spending on Amtrak, PBS, and the NEA and reducing federal compensation appears to offset the $109 billion in lost revenue from repealing Obamacare, resulting in at least $211 billion in savings by 2022. (That's assuming that program spending levels and federal compensation remain constant over the next 10 years, so it's just a back-of-the-envelope calculation to get a sense of the magnitude of these cuts.)

But that's still a very long ways off from achieving the $9.6 trillion in non-defense cuts that Romney's budget would demand: $211 billion in spending reductions, for instance, would be about 2 percent of the total cuts necessary. What's more, in the same Fortune interview, Romney promised that "infrastructure is going to see very substantial investments over the coming decade," suggesting that he wouldn't cut funds from that area either. And the other specific cuts that Romney has publicly detailed — to Planned Parenthood, foreign aid, etc. — are similarly small.

So Romney still has a lot of explaining to do about how he would actually make the cuts that his own budget demands, as the spending reductions he's specified so far would only make a small dent, at best.