With debt-reduction talks in disarray, Democrats and Republicans should adopt a new approach: pursue savings by strategically reorganizing the vast federal government. Not only could this produce as much as $1 trillion in savings, but it could create bipartisan momentum to clear the way for harder future choices on taxes and spending.

A reorganization package would give President Barack Obama the government overhaul he promised in February, while House Republicans would get many of the bureaucratic reforms they promised in last year's midterm campaigns. Reorganization hasn't been on the table, though, since even members of Congress consider it technical and boring. Yet here's a model that hits a hard target of $1 trillion in savings over the next 10 years:

• Cut federal jobs. Flatten the number of federal management layers to no more than six. In a 2005 study, I found an average of 18 layers between, say, the secretary of agriculture and the forest ranger, or the secretary of the interior and the oil-rig inspector—up from seven layers in 1960. Washington should also cut the number of presidential appointees and senior and midlevel managers by a third, and establish a pay-as-you-go system to keep all these changes in place. Possible savings, from saved compensation and higher efficiency: $100 billion.

• Freeze all hiring at the senior and middle levels of government. New hires should be made only if the president certifies that a given vacancy must be filled in order to meet one of the national priorities set by the recently enacted Government Performance and Results Modernization Act. Possible savings: $250 billion.