More than perhaps at any time in recent American history, questions of budgeting and the country’s financial future occupy center stage. We have seen, in recent weeks, a long-delayed deal on the 2011 federal budget that stripped $38 billion out of so-called “nondefense discretionary spending,” which includes most of the domestic programs Republicans love to hate (aid to the poor, environmental protection) and accounts for 12 percent of the roughly $3.5 trillion budget. The government came within one hour of shutting down, and this evidently led to some giddiness in the White House, which produced, on April 9, a perplexing video from President Obama in which he almost seemed to boast about the “largest annual spending cut in our history.”

Then, actually, right in the midst of that drama, came the manifesto—“The Path to Prosperity,” he called it—of Paul Ryan, the Wisconsin Republican who chairs the House Budget Committee. Ryan claimed that he would cut $5.8 trillion in spending over the next decade from current projections by the executive branch’s Office of Management and Budget (OMB). Ryan forced the hand of Obama, who had been exasperatingly silent on the whole budget mess except for his brief video. On April 13 Obama announced his own scheme to wrench $4 trillion in savings out of the budget over twelve years.

The urgency is justified—to an extent. The OMB estimates a budget deficit of $1.65 trillion this year, or 10.9 percent of Gross Domestic Product, more than double what it was before the Great Recession starting in 2007. The country’s debt is now $14.3 trillion, and will go up soon. Publicly held debt is at 72 percent of GDP, having averaged about 40 percent during the previous ten years. And spending on entitlements, particularly Medicare, will rise dramatically as Baby Boomers retire. While the alarms raised in Washington by people who thunder that entitlements especially must be examined can be hyperbolic, it is certainly the case that the long-term fiscal picture needs to be addressed.

The question is how. Everyone talks about cutting. Washington is awash in numbers of various kinds, but here are two, both from the Center on Budget and Policy Priorities (CBPP), a liberal policy analysis group whose work is respected across ideological lines, that seem especially relevant. I have not seen them paired together, but when they are, they describe for me better than any other numbers why we’re in the fix we’re in, what needs to be done—and why the budget battles coming this fall and next year will determine not only whether Barack Obama can get himself reelected but whether the American welfare state that was built in the twentieth century will survive.

In 2008, the “Center on Budget,” as Washingtonians call it, released a report finding that keeping George W. Bush’s tax cuts intact through 2018 would cost $4.4 trillion. (Particularly controversial is the Bush tax cut lowering…