After a few weeks of posturing, House Speaker John A. Boehner, R-Ohio, finally agreed to increase tax rates on the highest-income Americans. Although his offer stopped almost half a trillion dollars short of President Obama’s proposal, the mere fact that the GOP’s top negotiator would support an increase in those rates at all brightens the prospects for a deficit-cutting deal by Jan. 1.

But it may prove easier for the two parties to reach agreement on taxes than on spending, particularly when it comes to entitlements. Some Democrats have spent weeks lobbying Congress not to touch the largest benefit programs or cut government jobs. That’s just not realistic. And if the two parties don’t get serious about both sides of the ledger, Washington will wind up with a deal that’s too small to bring the government’s burgeoning debt under control, or with no deal at all.

The negotiators’ short-term goal is to avert the potentially recession-inducing across-the-board tax hikes and spending cuts due to take effect automatically at the end of the year. Their longer-term goal should be to shrink the deficit enough to stop the debt from growing faster than the U.S. economy. Reduced unemployment will help on that front, as will the withdrawal of U.S. troops from Iraq and Afghanistan. But even accounting for those changes, budget experts say that Washington still has to cut projected deficits by about $4 trillion over the coming decade to hold the debt steady as a percentage of the economy.

Boehner called for cutting projected spending by $1 trillion over 10 years while raising an equal amount in new tax revenue, in part by ending the Bush-era tax cuts for those making $1 million or more. Obama had sought $400 billion more in tax revenue, or $1.4 trillion over 10 years. Yet even if the GOP eventually comes closer to Obama’s tax proposal, lawmakers will still have to reel in spending considerably to stabilize the growing debt. The biggest problems for the budget are Medicare and Medicaid, the healthcare benefits whose costs are growing rapidly. Unless Congress finds a way to shore up those programs, the federal budget gap will only get worse in later decades.

The spending cuts and tax hikes can’t be so steep that they crush the struggling economy. If lawmakers come up with a credible plan to reduce the deficit over time, however, they should ease the anxiety and uncertainty that has deterred risk-taking by businesses and slowed the recovery. A truly credible plan would require Republicans to vote for higher taxes and Democrats to vote for cutting entitlements, imposing political costs on both. Boehner and Obama shouldn’t waste the effort on a plan that stops short of solving the problem.