A House staffer hands out copies of the Republican 2012 budget proposal (Joshua Roberts/BLOOMBERG)

No, budgets are a moment when the two parties can’t hide. They’re a moment — one of the only moments — when politicians stop talking and put numbers down on a page. Numbers we can check and see and question. And so they should be read closely, and mined in great detail, because in those numbers -- in the tables in the back, and the assumptions fed to the Congressional Budget Office -- we can see the decisions the parties make when they’re forced to choose between competing priorities and constituencies. In those numbers, we can see, with unusal clarity, what the fights that animate American politics are ultimately about.

But the numbers don’t matter if we don’t force them off the page and into the world voters actually inhabit. Which brings us to David Brooks’s Friday column:

Under Ryan, Obama charged, 10 million college students would get their financial aid cut by $1,000, Alzheimer’s research would be slashed, 200,000 children would lose their chance to enter Head Start.

Where did Obama get these specifics? He imagined them. He imposed some assumptions that are nowhere to be found in the Ryan budget. He compared Ryan’s reduced spending increases with proposed growth, not current levels.

Brooks is right: Obama did offer specific cuts that don’t appear anywhere in Ryan’s budget. But only because Ryan refused to provide the specifics himself.

Ryan has said how his cuts will be distributed on the category level. He’s clear on the size of hit that “non-defense discretionary spending” will take. But he hasn’t said how those cuts will be distributed among the programs in that part of the budget. His numbers stop at the water’s edge of the real services and programs people use. And so the White House, to try and make them real, made a assumption — arguably, the only assumption they could make: They assumed that when Ryan said he would cut X category of spending by Y percent, those cuts would be dsitributed equally among the programs in that category. And the Ryan camp — echoed here by Brooks — called foul.

As it happens, I’ve spent the last 24 hours trying to unravel the Ryan camp’s argument that the White House is imposing unfair assumptions on their budget. In particular, the assumption they’re upset about is the White House’s claim that their budget will mean 10 million college students get their financial aid cut by $1,000. Unpacking this gets a little complicated, and it requires getting into some budgetary weeds, but it’s also a good case study of what happens when you start trying to estimate the Ryan budget’s effects on real programs.

Under current law (pdf), Pell grants are scheduled to receive $30.5 billion in 2014. $24.5 billion will come from “discretionary spending.” $6 billion will come through “mandatory spending.”

Ryan’s budget says that Pell grants “would be fully funded through discretionary spending.” And it says that the category of discretionary funding that includes Pell grants will be cut by 19 percent. This leaves two options for what happens to Pell grants:

- Ryan’s budget erases all the funding they get from the mandatory side of the budget and then cuts their discretionary funding by 19 percent. That would blow a $12 billion hole in the program. That’s what the White House assumed.

- Ryan’s budget doesn’t cut Pell grants by 19 percent. Instead, it cuts them by somewhat less than 19 percent, but it it cuts other domestic discretionary programs by much more than 19 percent. That’s pretty much what Ryan’s office is arguing.

So there are two choices here: You can believe that Ryan cuts Pell by as much as the White House says he does, or believe he protect Pells from some portion of the cuts and increases the cuts to other programs by a commensurate amount.

If you read pages 86-87 of this budget document, I’d say door number two has it. In his “illustrative policy options,” Ryan proposes that Congress “roll back certain recent expansions” and “consider a maximum income cap” and “eliminate eligibility for less-than-half-time students” and adopt a lower “maximum award level.” He would keep the current maximum grant of $5,550, which is lower than the scheduled maximum grant of $5,635.

Ryan doesn’t give a total cost estimate for the program. But it’s safe to say that while he’s cutting it substantially, he’s not cutting it by the $12 billion the White House assumes.

However, if he’s not cutting Pell by as much as the White House thinks, he’s cutting other things by more. But he won’t say what. Obama “imposed” the simplest of all assumptions: Equal cuts across-the-board. I think Brooks would agree that it would have been far more unfair for Obama to guess at which programs would have taken a big cut, and which programs would take a small one.

There’s a bottom line here: You can’t cut spending without cutting spending. But Ryan wants to have it both ways: He wants to get the credit for cutting spending, but he doesn’t want to have to propose specific spending cuts. Oh, and he doesn’t want anyone to extrapolate what those cuts would be, either.

Of course, even Ryan’s supporters should see the problem here. If these cuts are too unpopular to detail, then they’re going to be too unpopular to pass. If the only way to defend Ryan’s budget is to beat back any attempts to make it specific, then it’s an empty, useless document.

If Ryan’s budget is to pass, the defense has to be that his cuts are worth it, or necessary, or wise, or, at the least, better than the alternative. On Pell grants, for instance, his office accurately argues that the White House’s plans for Pell are unfunded after 2015. After that, it’s not clear where the money comes from. They also argue that the Pell program isn’t well targeted, and that increasing student aid so quickly is driving up the cost of tuition. And they argue, more broadly, that debt and tax increases pose such dangers to the American economy that dramatic, painful cuts are a superior option.

These are all arguments we can, and should, have. But in the end, we’re also going to have to have an actual discussion of how and where Ryan intends to make his cuts. And a discussion of where Ryan is going to find the $4.6 trillion to pay for his tax cuts.

To try and protect Ryan from that discussion -- to attack the simple, assumptions required to turn Ryan’s budget into a specific, comprehensible document -- is to give up on all the rigor and clarity that the two budgets can bring to our national debate, and to let the two parties retreat back into the bromides and press releases that allow them to so effectively obscure their visions, and our choices.

And it is also, in the end, to say that Ryan’s budget is not defensible, or at least it requires choices that cannot be defended to the public. That would be an interesting revelation -- and it would mean Ryan’s budget has told us something important about the workability of his vision — but I don’t think it’s the point Brooks is trying to make.