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The continued inability of President Obama and House Republicans to reach some sort of compromise in the budget wars has inspired an endless stream of advice, pleas, psychoanalysis, and befuddlement. Why oh why can’t the two sides meet in the middle somewhere?

The impasse has many causes, but the most fundamental of them may be that the entire left-right conception may be misplaced. If the goals of the two parties can be plotted along a left-right axis, then a sane negotiation ought to locate some sort of midpoint — a bit more tax here, a bit less spending there. But the release of the budget documents, first by House Republicans and then by Senate Democrats, suggests that the disagreements don’t lie along a simple left-right axis. The parties can’t find a middle ground because a middle ground does not exist.

Begin with President Obama’s goals. He has three:

1. As economic adviser and Bob Woodward threatener Gene Sperling recently explained, Obama believes that the long-term rise in spending on retirement programs crowds out the government’s ability to spend money on other things, especially investments in research and infrastructure. Of course, part of the solution is to raise taxes and spend more money on both investments and retirement programs, but raising taxes is politically painful and therefore justifies cutting retirement programs below the preferred level in order to get the revenue.

2. Obama believes the deficit is entirely a long-term problem, and that reductions should be delayed so as not to hamper the recovery. Ideally, long-term deficit cuts would be paired with an immediate, temporary stimulus.

3. Obama’s highest priority is that the long-term fiscal correction doesn’t worsen income inequality, the long-term rise of which he regards as a significant social problem. That principle dictates that cuts to retirement programs both be limited in scope, so as not to undercut their basic social insurance role, and balanced with higher taxes on the affluent. Most important to Obama, deficit reduction should spare benefits for the most desperately poor and sick Americans.

The distinction with the Republican approach as embodied by Paul Ryan’s budget is sharp. Consider where Ryan stands on these three points.

1. Obama wants to clear out more budget headroom for public investment, but Ryan proposes to subject domestic discretionary spending, which is already slated to fall to the lowest level as a proportion of the economy in four decades, to what the Bipartisan Policy Center calls “enormous reductions” of over a trillion dollars. Moreover, Obama is willing to offer up more cuts to Medicare, but as influential Ryan adviser Yuval Levin explains, Ryan doesn’t want to find more savings in the traditional Medicare program. He is focused on what he considers the transformative power of voucherizing the system. And even though Ryan’s plan would continue traditional Medicare for anybody over 55 years old — that is, leaving it in place for five decades — Ryan considers it pointless to spend less money on it. Indeed, worse than pointless. Since Obama’s proposals to require more efficiency out of traditional Medicare require “government bureaucracy,” this is ideologically alien to Ryan and thus, writes Levin, “steps in the wrong direction.” A more cynical observer than Levin might note that the more success we have in making traditional Medicare more efficient, the weaker the case will be to phase it out and replace it with some form of vouchers.

This is a crucial problem. The thing that Obama regards as his biggest potential concession to Republicans is greeted by Republicans as not a concession at all.

2. Rather than postponing his cuts to avoid economic contraction, Ryan would implement his immediately. Indeed, he rejects the entire economic principle that immediate spending cuts can reduce economic demand as, in a term he used in an interview yesterday, “sugar high economics.” Or, as fellow Billy Long Republican told Politico, Obama “said the short-term debt’s not that bad, and we think it is that bad.”

3. Where Obama insists that deficit reduction not widen income inequality, Ryan views it primarily as an opportunity to widen income inequality. Indeed, the inequality-widening characteristics of his budget are far more concrete than its deficit-reducing characteristics. Ryan’s plan reserves its largest cuts for programs targeted to the desperately poor and sick. He would cut the budget for Medicaid and Childrens’ Health Insurance by more than half, increasing the uninsured population by 40 to 50 million. He proposes a “goal” of cutting the top tax rate to 25 percent, offset by unspecified reductions to tax expenditures. The most generous reading of this tax proposal is that he would pour every dollar of savings from tax reform into rate cuts that would shift the tax burden down from the very rich, who benefit the most from lower rates, onto the middle class. The less generous reading is that Ryan wants to cut tax rates without paying for it, which is the policies he supported under President Bush.

In either case, Ryan views budget reforms as primarily an opportunity to defend the makers from the takers, and only secondarily as an exercise in fiscal balancing.

Viewed in this light, the impasse looks very hard to bridge. Obama and Ryan aren’t proposing different solutions to the same problem. They are attacking completely different problems, and the things each of them defines as a problem, the other side does not. The only path to agreement would seem to involve Obama going around Ryan and picking off a minority of Republicans unable to stomach sequestration and willing to compromise. Consummating a deal with Ryan seems ideologically impossible.