Paul Ryan, in his latest House budget plan, is certainly ambitious in his goals.

Balance the budget in 10 years. Avoid the military cuts occurring in the current federal “sequester.” Streamline the tax code without raising taxes. Make entitlement programs sustainable. Make the public debt go down, not up.

Representative Ryan urged all those things Tuesday and more, in his role as chairman of the House Budget Committee. The targets in the committee’s new budget plan are in some cases hard to achieve simultaneously.

And they’re controversial. Ryan blended candor with understatement when he said President Obama would “probably not” sign on to all the Republican ideas. The White House didn't disappoint, saying in a statement that the budget's math "doesn't add up" and that Mr. Obama considered the proposal "the wrong course for America."

Here’s a tour of Ryan’s proposal, with each stop headlined by an eye-popping number from the House budget document.

Net interest on national debt in 2023: $630 billion

That’s how much the nation would spend on interest payments alone, during the 2023 fiscal year, even if Ryan’s big spending cuts were enacted and the nation balances its budget.

Without any change from current policies, debt payments in that year would total $857 billion, the Congressional Budget Office (CBO) calculates.

Unless the buildup of debt is addressed, “we are consigning the next generation to an inferior standard of living,” Ryan said Tuesday.

Although they might not phrase the consequences exactly that way, nonpartisan economists including those at the CBO generally agree on the need to address the national debt.

Most economists agree that the core cause of the rising national debt is entitlement spending that’s growing fast, as a share of overall national income, without tax revenue to cover the cost.

Annual rise in Medicare spending per capita: GDP growth plus 0.5 percent

Ryan’s controversial idea of overhauling Medicare isn’t new, but his approach gives a jolt to anyone accustomed to the current system. He says he’s saving Medicare from its current track of “going bankrupt.” Critics say he’s turning a vital piece of economic security for seniors into a voucher program.

Ryan’s new budget plan calls for a shift toward a “premium support” model of Medicare, starting in 2024 for people born in 1959 or later. Seniors would choose among a variety of health plans, and Medicare would provide a premium-support payment that would cover all or part of the insurance.

The pace of Medicare spending would slow, because annual increases would be capped at the rate of GDP growth plus 0.5 percent – well below their long-term trend line. Low-income Americans would get extra help with out-of-pocket costs.

“This proposal would use competition – not bureaucratic fiat – to control costs,” the budget plan says.

Where the CBO forecasts $8 trillion in Medicare spending between 2014 and 2023, the new House budget plan calls for $6.6 trillion in net Medicare spending for that period.

Expanding the federal safety net: zero dollars

A section of the House Republican plan is titled “safety net strengthened.” The Ryan approach is defined by the argument that the current array of antipoverty programs hasn’t put much of a dent in poverty, and that a focus on stronger economic growth would do the most to improve living standards at all income levels.

Practically, though, that translates into what liberals and some other budget experts say are harsh cutbacks in programs including Medicaid for the poor. The plan calls for a repeal of the Affordable Care Act (“Obamacare”), including its expansion of Medicaid coverage to more Americans.

The impact? A CBO baseline sees Medicaid spending at $572 billion in 2023 plus $134 billion for insurance subsidies to help households buy insurance under Obamacare. The House budget would provide $387 billion in that year for Medicaid and other non-Medicare health programs.

The House budget also sees “other mandatory” spending (which includes supports for the poor such as food stamps) falling from $443 billion in 2014 to $404 billion in 2023.

Converting SNAP (food stamps) into a block grant to states, indexed for inflation and eligibility, “allows states to tailor their programs to their recipients’ needs,” while encouraging recipients to find work, the House plan says.

Defense funding for a decade: $6 trillion

The Ryan plan calls securing citizens’ safety the “first job of the federal government.” It calls for adding back about $500 billion in defense cuts that would be in place if the automatic reductions of the Budget Control Act (reductions known as the “sequester”) remain in effect.

Still, the House budget seeks less for defense than the Ryan-led committee did last year. Ryan says the plan fully funds defense needs that have been outlined by the military’s joint chiefs of staff.

Going after waste: $115 billion in “improper payments”

The Budget Committee cites research tallying $115 billion in “improper payments” to individuals or contractors from the federal government in 2011. This includes a range of problems from Medicare fraud to unintentional wrong payments. But it’s not all pure waste – some of this money is the right amount, being sent to the right place, but with improper record keeping.

Targeting this problem is part of a larger initiative Ryan calls for, to improve the fairness of federal programs by eliminating waste and special-interest handouts – and saving money in the process.

The effort includes rolling back corporate subsidies across the energy sector (Ryan says the handouts have been especially generous to green-energy firms) and reforming the role of government in mortgage financing. The Republican plan says the loan guarantees provided by Fannie Mae and Freddie Mac, with taxpayers as a backstop, should be "drastically" decreased. Some critics of this idea say this could push up mortgage interest rates.

Only two tax brackets: 10 percent and 25 percent

The House Republicans call for simplifying the tax code. The aim is to raise the same amount of tax revenue, but in a way that better encourages economic growth – by keeping marginal tax rates low. Payers would be divided into two tax brackets, one paying at a 10 percent marginal rate and the other at a 25 percent marginal rate.

Critics level a similar charge that they did against presidential candidate Mitt Romney: that the change could bestow extra benefits on upper-income Americans who are now being asked to pay a 39.6 percent top tax rate.

Ryan asserted, as Romney did last fall, that this problem can be addressed by rolling back tax deductions more for the rich than for everyone else.

Total federal spending over 10 years: $41.5 trillion

Total federal spending would be about $4.6 trillion lower than the baseline the committee started with, and $5.7 trillion less than a CBO baseline.

So, if you aren’t convinced yet, the Ryan plan involves big budget cuts. Total spending would be higher, in dollars, in 2023 than it is today. But as a share of the economy, outlays would fall to match revenues of roughly 19 percent of GDP.

Discretionary spending wouldn’t keep pace with inflation.

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The benefit: Debt, which many economists see as already in a zone where it endangers economic prosperity, would fall from about 73 percent of one year’s GDP down to 55 percent.

The drawback is the squeeze on both entitlement programs and discretionary priorities. Where Ryan says these are tough but necessary choices, critics say there’s no reason the budget has to balance by 2013, or why some of the reduction in deficits can’t come from tax hikes.