Keynesians and Dose-Dependent Responses

A repeated argument we hear from the Keynesians for why Keynesian solutions do not work, like say Japanese efforts to revive their economy during the "lost decade"—a policy which Obama is showing signs of embarking upon—is that they weren't Keynesian enough (example).

Say a Keynesian economist recommends a certain sum be infused to jump-start the economy, and have it humming again. But government agencies didn't spend that much. When they had spent a quarter of the recommended amount, almost nothing happened. When they were up to a half, not only did nothing happen, but there was a deterioration in economic activity. But, Keynesians say, if the whole amount had been spent, things would have been fine.

This would be a non-"dose-dependent" response, meaning there is non-linear relationship between the treatment applied, and the response outcome. In other words, small expenses don't lead to small gains, but they suggest large expenses would lead to large gains.

Keynesians need to explain why this is so before it would make any sense to choke on a full dose of Keynesian medicine.