Would higher inflation fix our economy?

Should the Fed purposely cause higher inflation for a while as a way to reduce unemployment? This is an idea I've seen from various economists lately, which I originally read from Greg Mankiw, who is now Mitt Romney's economic adviser.

We typically have a knee-jerk reaction that higher inflation is bad. But what effects would it have if money started losing its value more quickly? Because of the uncertainties of our bad economy, people are saving more of their money instead of spending or investing it in ways that would produce growth. But higher inflation would give more incentive to spend/invest that money, because otherwise it will just sit there losing its value. This would also benefit those who are in debt (at the expense of lenders) because it effectively reduces how much they really owe.

Obviously, you shouldn't make inflation too high because of the clear downsides. But if you assume the view of our economic problems that I recently posted, where high household debt and low spending are keeping us from a recovery, then it does seem that a move towards somewhat higher inflation would have an overall positive effect for the reasons above. It's effectively similar to fiscal stimulus but with 2 advantages: it wouldn't add to our national debt, and it wouldn't require passing a bill through the children in Congress. However, the Fed has shown no intention of using this strategy, even though Bernanke supported the idea in the past as a way for Japan to pull out of its slump in the 90's.