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Virginia Gov. Bob McDonnell sits on many potential VP lists but problems might be brewing in his home state where his approval rating has slipped in the past 12 months, according to a new Washington Post poll.

His approval rating dropped to 56 percent from 62 percent in the past year, the poll found, and 35 percent of Virginia voters disapproved of McDonnell's work in the state, a 9 point increase from last year.

McDonnell, who is barred by Virginia statute from running for a second term, still enjoys a high approval rating compared to other governors, but the drop comes after a difficult year in the state legislature and a controversial ultrasound bill that brought national attention to the state. He assumed office in January 2010 after three years as state attorney general.

The Virginia governor and retired Army lieutenant colonel, 57, has the support of 52 percent of the state's women, a constituency with which presumptive Republican presidential nominee Mitt Romney is looking to boost his own standing this fall.

And would a Romney-McDonnell ticket help turn out independent voters in the key battleground state of Virginia? Seven in 10 independent voters said that adding McDonnell to the GOP ticket would not affect their pick in November.  Eight percent said McDonnell's spot on the ticket would make them vote for Romney while 18 percent said they'd opt for Obama.

McDonnell's PAC, Opportunity Virginia, recently placed a substantive ad buy intending to highlight the job growth and economic prosperity of Virginia.  McDonnell's team denied that such spending was an attempt to boost his approval ratings before Romney's selection of a running mate.

Read more here about McDonnell's ascent to the governorship here.