I mean you are right, that an increase in the savings rate has something to do with net exports and investement, as the saving has to be put somewhere. But savings is the trigger, the thing which people decide to do. Investment isn't too strongly dependent on local savings rates. If you want to borrow money for an investment and nobody in your country saves, you may import the money from another country where people do save.

And given that, there is no reason, why the output should not go down, when people start to save more money. There will be less demand for foreign financing of US investment, but when they buy less domestic products, the producers will produce less. If in the US something similar happens as in Germany from 2003 - 2005 I would call it trouble in the short term.

Of course in the long term that is the right thing to do, still.

To the second, this is clearly wrong.
You can increase your savings rate without higher income, when you stop buying stuff you formely bought regularly. This is what must happen in the US. People there (aggregated, just to mention, that nobody complains he didn't) have lived quite a lot beyong their means. The time of recognizing this is close, either somewhat voluntarily now, or forced in a few years.

Der Amerikaner ist die Orchidee unter den Menschen
Volker Pispers