Nonsense.
http://forums.about.com/n/pfx/forum.aspx?nav=messages&webtag=ab-urbanlegends&tid=10312Most mayors have very little power, and if you look at this a little differently, taking note of poverty by counties, most of the worst are in the South and lean toward Republicans.
For what it's worth, here are the 10 "poorest (by unemployment rates)" states and the party of the Governor:
1. Nevada (14.2%) Sandoval is the current governor, the state has had a Republican since 1999.
2. Michigan (13.2%) Rick Snyder, Republican (currently being recalled )
3. California (12.3%) Jerry Brown, the once and future governor, a sort of Democrat. To be fair, Schwarzenegger was the Republican governor until very recently.
4. Rhode Island (12.0%) Lincoln Chaffee, newly minted Independent, but they've had a Republican governor since 1995
5. Florida (11.4%) Technically Republican
6. Mississippi (11.0%) Haley Barbour, Republican, governor since 2004
7. South Carolina (10.7) Mark Sanford, R, since 2003, Nikki Haley, R, current
8. Oregon (10.5%) John Kitzhaber, D. The last Republican governor was in 1987
9. Ohio (10.5%)Newly elected John Kasich. R. Following Ted Strickland, D, who served a single term and was preceded by R's going back to 1991
10. Illinois (10.4%) Pat Quinn, D. Follows corrupt governor Blagojevich, D, who was preceded by Republicans going back to 1977.
Now there are also many different questions that need to be asked in the field of statistics, such as "Is X voting Y because they are poor, or is X poor because they are voting Y, or is there any actual influence from either on either". But of course the meanings of statistics don't make nice little political talking points, they do require you to think after all instead of copy & pasting.
EDIT: Forgot to add my source, the unemployment numbers come from the US Department of Labor June 2010 with a quick dose of Wikipedia to check the political affiliation of each states Governor