According to Marist:

Former Alaska Governor Sarah Palin may still be making news headlines, but the U.S. electorate has news for her. If the 2012 presidential election were held today and she were the Republican candidate, Palin would not defeat President Barack Obama. In fact, the president would win the election by a considerable margin.

56% of U.S. registered voters report they would cast their ballot for the president while 33% would vote for Palin. It’s probably not a shock that public opinion divides along party lines. 92% of Democrats would support Obama in this hypothetical contest while 73% of Republicans would back Palin. Although President Obama does not receive a majority of Independents in this matchup, Obama does win nearly half — 49% — of this key voting group. Palin receives 34% of their support.