A new Rasmussen survey suggests that former Alaska Republican Gov. Sarah Palin would lose her home state if she were to run for president, and by a sizable margin.

Rasmussen interviewed 500 likely voters and found that “just 41% say they would vote for the former Alaska governor if she ran for president in 2012. Forty-eight percent (48%) say they would not vote for Palin, and 11% more are undecided.” Due to the small sample size,the margin of error for the survey is 4.5 percent, plus or minus.