ON NOV. 16, PRESIDENT Obama and congressional leaders of both parties emerged from their first post-election sit-down pledging to find a compromise on the budget.

The tone of reason has made purists on both sides of the aisle nervous. Grover Norquist, leader of the never-raise-taxes brigade, is insisting that Republicans give no ground. Three big unions have launched an ad campaign warning moderate Democratic senators not to countenance any cuts to Medicare, Medicaid, Social Security or education. “Voters are going to be watching,” an official with the Service Employees International Union warned during a conference call with reporters Tuesday.

No doubt there is a tactical element to the positioning on both sides. Union leaders and others on the left may understand Mr. Obama will have to accept some reform of entitlement programs. Anti-tax activists may understand House Speaker John A. Boehner (R) will have to accept higher revenue. By stating maximalist positions, both sides may calculate they can enhance the bargaining position of the leaders and minimize the concessions their side has to make.

But the effect of their politicking may be to block any compromise — to prevent a sufficient number of legislators from making the hard decisions needed to put the country on a sound financial footing. Without compromise in the short term, the nation will tumble over the fiscal cliff — the series of sharp tax hikes and spending cuts due to take effect Jan. 1 — that the Congressional Budget Office (CBO) says would send the nation back into recession. Without compromise for the longer term, the country faces a future in which more and more revenue goes to pay interest on the debt and less is available for health care, defense or anything else.

Compromise is essential for political reasons; with Republicans controlling the House and Democrats the White House and Senate, there's no alternative. But more to the point: Compromise is essential to make the numbers work. If you don’t raise taxes to some extent, you have to make intolerably deep cuts to Medicare, Medicaid, Social Security and the other entitlement programs that make up 60 percent of the federal budget. If you don’t make any cuts to those programs, you have to raise taxes to levels that no one could support.

Here’s how the nonpartisan CBO explains things: “It is possible to keep tax revenues at their historical average percentage of gross domestic product — but only by making substantial cuts, relative to current policies, in the large benefit programs that aid a broad group of people at some point in their lives. Alternatively, it is possible to keep the policies for those large benefit programs unchanged — but only by raising taxes substantially, relative to current policies, for a broad segment of the population.”

Bottom line: “Ultimately, significant deficit reduction is likely to require a combination of policies, many of which may stand in stark contrast to policies now in place.”

Ironically, the purists on both sides defend their positions by saying they are promoting economic growth — the right by cutting taxes, the left by “investing in jobs,” by which they mean more government spending. They’re both right that economic growth is the best way to reduce the deficit, and that policymakers have to take care not to snuff out the fragile recovery underway. But it’s more than misleading to suggest growth offers some magical way around a budget deal. Even under the most optimistic growth scenarios, there is no way, given the aging of the population, to curb the debt without slowing entitlement growth and raising taxes. That’s the fundamental truth.