The connection between the US Saving Rate and the unemployment rate has historically been positive - rising unemployment coincides with rising household saving. This is due to the fact that as because households temper spending, firms reduce hiring, thereby increasing unemployment.
As saving and unemployment rates remain below trend, it's unclear which of the two will rise first. My suspicion is that we've reached trough saving rates in the U.S. (between 2%-3.5%) and that this fact portends a rise in the unemployment rate in coming quarters. QE unwinding might complicate this analysis, however.
For the those so inclined, here is a GitHub repository examining the relationship between personal saving and unemployment: https://github.com/benlusamba/macroquant