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President Obama has gone coast to coast this week stumping for his new budget proposal, a plan that he hopes will shrink the government's ballooning debt. Republicans are pushing their own plan developed by House Budget Committee Chairman Paul Ryan. And sorting through their conflicting claims is no small task.

So we asked NPR's John Ydstie for some help.

JOHN YDSTIE: Even in the best of times, budget plans arrive in a blizzard of numbers. When the country faces daunting fiscal challenges, as it does now, the storm gets even more blinding. Here's President Obama unveiling his plan last week.

President BARACK OBAMA: So this is my approach to reduce the deficit by $4 trillion over the next 12 years. It's an approach that achieves about $2 trillion in spending cuts across the budget.

YDSTIE: The president goes on to tout a $1 trillion reduction in interest payment on the debt and another trillion in cuts to so-called tax expenditures.

A week earlier, Chairman Ryan used visual aids to launch his budget.

Representative PAUL RYAN (Republican, Wisconsin; Chairman, House Budget Committee): Now, let me walk you through some of the charts and some of the numbers. If you take a look at the screens on the side here, first of all, let's look at spending.

YDSTIE: Ryan goes on to summarize 5.8 trillion in spending cuts and $4.4 trillion in deficit reduction.

So both the president and Chairman Ryan are claiming around $4 trillion in budget savings, that seems clear. But, says Maya MacGuineas of the bipartisan Committee for a Responsible Federal Budget, it's not that simple.

Ms. MAYA MacGUINEAS (President, Committee for a Responsible Federal Budget): The question is saving compared to what? And that's where you get lost in the confusing, crazy world of budget baselines.

YDSTIE: For instance, by law, Chairman Ryan is required to use the Congressional Budget Office baseline as his starting point, but that baseline presumes the expiration of the Bush tax cuts at the end of 2012 and continued high-level spending on the wars in Iraq and Afghanistan for the next decade, neither of which is likely.

Further complicating things, President Obama's new proposal makes a number of changes to that baseline. So the $4 trillion in deficit reduction they both claim aren't directly comparable.

MacGuineas' group decided to crunch the numbers for both proposals using a common baseline and the standard 10-year time frame, not the 12 years the president is using. It found that the president's plan saved about half as much as Chairman Ryan's.

Ms. MacGUINEAS: A little bit less than two and a half trillion dollars over the same period, so an apples-to-apples comparison brings a lot of things to light.

YDSTIE: That's largely because a big share of the president's savings come in the 11th and 12th years of his plan.

Clint Stretch, who's a budget specialist at Deloitte, a consulting and financial advisory firm, says there's another way to get a handle on what a politician is doing in a budget proposal. Ask this question.

Mr. CLINT STRETCH (Tax Principal, Deloitte Tax LLP): What are they saying about the level of spending and the level of tax that they desire to have as a share of the economy, as a percentage of GDP?

YDSTIE: That number tells you the size of government that the politician imagines in the future. Chairman Ryan's proposal would lead to a shrinkage of government from almost a quarter of the economy right now to under 15 percent 40 years from now. That's about the size of the government back in the 1950s before Medicare and Medicaid.

President Obama has a very different view, says Stretch.

Mr. STRETCH: The president is saying, no, you know, the population is getting older. We've made a lot of retirement promises. We ought to try to keep those. And so the government will get bigger because we have more people in retirement.

YDSTIE: How much bigger? A couple of percentage points above the long-term average. Clint Stretch admits that in a $16 trillion economy, these numbers are hard to get your head around.

Mr. STRETCH: And so for a lot of people, the more important question is: Are the spending recommendations and the tax recommendations that are made, do they seem like they are about the kind of country that you would like to live in?

YDSTIE: For instance, do you want more spending on defense and less on health care for the elderly? Or do you want to spend more on both? And finally, is this a vision of the future you're willing to pay for?

John Ydstie, NPR News, Washington.

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