One of the key Republican criticisms of last year’s health-care law—the Patient Protection and Affordable Care Act, or PPACA—was that its Medicare cuts were so aggressive as to be illusory. Skittish future Congresses would surely repeal these cuts, Republicans argued, so PPACA would wind up widening the federal budget gap despite the Congressional Budget Office’s rosy projections. But this year, both House Republicans and President Obama are advancing budget plans that rely on Medicare costs’ growing even more slowly than they would under PPACA. Their proposals are thus vulnerable to the same criticism. Congressman Paul Ryan, who has led the House effort, has offered a plan that makes clear the difficult choices that lie ahead and that includes some positive structural changes to Medicare and Medicaid. But his budget’s projections rely on an assumption that we can spend far less money than we had planned to run both programs—and those savings are too ambitious to be plausible under the reforms he proposes.

The most discussed part of Ryan’s proposal is his plan to convert Medicare from its traditional form to a “premium-support model” for people currently under 55. These people would receive government assistance to pay part of a premium for a health-insurance plan purchased through a federal exchange. Crucially, the value of this subsidy would grow only as quickly as the Consumer Price Index—even though CPI growth is generally expected to be about 2 percent, while per-capita health-care spending is expected to rise by 5 percent to 6 percent annually. As health-care costs rise faster than inflation, seniors would have to pay out of pocket for a greater share of their health costs each year, or consume less health care.

This premium-support model, however, wouldn’t begin until 2022. Before then, Ryan proposes to spend $389 billion less on Medicare through 2021 than the president’s budget proposal would. But Ryan’s budget, like the president’s, would keep the Medicare cuts from PPACA—the same ones that, Republicans complain, are wishful thinking. And both budgets would also make the “doc fix,” a rise in physician-reimbursement rates that Congress regularly implements.

Where, then, would Ryan’s $389 billion come from? He doesn’t advance a specific plan, though Alan Simpson and Erskine Bowles made some suggestions in their report late last year that he could adopt. These include lower physician-reimbursement rates, mandatory rebates from pharmaceutical companies, and higher co-payments and deductibles. They also include tort reform, which Ryan’s plan does call for, and which Simpson and Bowles estimate would cut Medicare spending by $64 billion over ten years. These steps, though, would meet stiff political resistance. And Ryan’s proposal involves repealing some of the key cost-saving features of PPACA—the Independent Payment Advisory Board and the “Cadillac tax” on high-cost health plans—and doesn’t lay out a new agenda for cost control.

On Medicaid, Ryan’s numbers are similarly optimistic. In the current system, the federal government matches a percentage of what states spend on Medicaid. Ryan would convert that arrangement into a block-grant program in which states receive a lump sum from the federal government and set the terms of their own low-income health-care programs. To pay for costs in excess of that lump sum, states would have to levy their own taxes. That’s a good idea—but again, the rate of spending growth that Ryan envisions is too slow. In his plan, the growth of the Medicaid block grants would be linked to CPI and to each state’s low-income population. Health-care costs, meanwhile, would surely rise much faster than that, meaning that each year, states would either have to reduce the generosity of Medicaid or raise more state-level tax dollars to pay for the program. Eventually, the situation would become untenable.

The president, in a much more limited fashion, also relied on slower health-cost growth in his speech this week on deficit reduction. Part of his plan is to lower the target rate of Medicare spending growth from GDP plus 1 percent—as PPACA specifies—to GDP plus 0.5 percent. But like Ryan, he is light on details about how to achieve that, aside from his support for lower prescription-drug pricing.

Constraining the growth of health spending isn’t a lost cause, and leaders in Washington shouldn’t abandon it. But they have to be realistic when they come up with estimates of future spending growth. Previous proposals, such as Simpson and Bowles’s and Alice Rivlin and Pete Domenici’s, have tried to limit spending growth to the rate of GDP growth plus 1 percent, or to the average of CPI and medical inflation. These rates are already aggressively low, but they’re achievable. A growth trend in line with CPI, like Ryan’s, simply isn’t plausible.

Politicians must also create robust cost-control mechanisms. As economist Tyler Cowen has written, these fall into two categories: consumer-directed cost control and government-planned cost control. I share Cowen’s view that a mix of the two is what’s called for. (Those who support an entirely consumer-directed model should remember that private health-insurance markets haven’t exactly held the line on costs over the last 20 years.) PPACA and the president’s proposals to revise it don’t offer enough cost-control measures; the Ryan plan offers even fewer. And these mechanisms are supremely important: without them, spending targets—whether Ryan’s, Obama’s, or someone else’s—are just numbers on a page.

An opportunity for health-care cost control that has so far been overlooked lies in the tax code: if we reduced or ended tax preferences for health benefits, we’d lessen people’s incentive to consume too much health care, and costs would rise more slowly. Both Obama and Ryan have said, without specifics, that we should enact a tax reform that broadens the income-tax base, and Ryan has previously called for ending the exclusion of employer-paid health benefits from income tax and replacing it with a one-size-fits-all credit that doesn’t get bigger when you consume more health care. If he incorporates that idea into his budget proposal, he’ll be able to make a much stronger claim that his plan slows health-care cost growth.

It would be even better if Ryan dropped his proposal to repeal the Independent Payment Advisory Board. Yes, Republicans bristle at central planning of health spending. But Medicare is already a single-payer government health-insurance program, and Ryan’s plan would take more than 40 years to phase it out. While it’s still around, it’s hard to see why we shouldn’t protect the taxpayers’ interests by making sure that its expenditures are cost-effective.

As for Obama, he’s on the record against taxing health benefits. John McCain proposed to replace the health-care tax exclusion with a credit in the 2008 campaign, and Obama’s campaign endlessly demagogued that plan as a scary threat to “tax your health insurance for the first time.” But since then, Republicans have shifted from attacking Democrats’ Medicare cuts to calling for even bigger ones. It would be a good time for the president to do his own flip-flop and call for taxing health benefits—especially since such a move would make the tax code more progressive.

Both Ryan’s and Obama’s budget proposals have problems beyond the health-care issues. For one thing, they’re both vague (especially Obama’s). The president wants to tax too much and do so in a way that’s particularly economically damaging. Ryan is insufficiently aggressive about cutting the defense budget and probably too aggressive on nondefense discretionary spending. An eventual compromise plan might look a lot like the Simpson-Bowles report. But because our federal budget troubles are, first and foremost, health-spending troubles, making realistic estimates of health savings is the most important step in producing a budget plan that works.

Josh Barro is the Walter B. Wriston Fellow at the Manhattan Institute and a regular columnist for RealClearMarkets.