Despite her deficit with independents Palin does lead Sheen 49-29 overall. We also tested Barack Obama against Sheen and the President leads 57-24.
Sheen is one of the most unpopular figures we've ever polled on. 10% of Americans rate him favorably to 67% with a negative opinion of him. The only people we've ever found worse numbers for are Rod Blagojevich in Illinois (an 8/83 favorability spread), Jesse Jackson Jr. in Illinois (a 10/73 favorability), and Levi Johnston in Alaska (a 6/72 favorability). Sheen's -57 spread ties what we found for John Edwards in North Carolina the last time we polled him (15/72).
Sheen's unpopularity is pretty universal across party lines so it says something about the level of polarization in the country right now that Democrats would support him by a 44-24 margin for President over Palin and that Republicans would support him 37-28 over Obama. People may not have any respect for Sheen but they still think he'd be a better alternative than their opposing party's leading figure.
Obviously Charlie Sheen's not going to run for the White House but the Palin numbers are one of the more interesting benchmarks yet pointing to just how minuscule her chance at the Presidency would be even if she did decide to get into the race.