The CNN/Opinion Research Poll also found there is no front-runner in the race for the Republican nomination. The three potential candidates at the top are former Arkansas Gov. Mike Huckabee, the choice of 21 percent of those surveyed, former Alaska Gov. Sarah Palin with 19 percent, and former Massachusetts Gov. Mitt Romney with 18 percent.
Keating Holland, CNN's polling director, said name recognition is a big factor in polls taken while the first primaries are still a year away.
"Keep in mind that Joe Lieberman and Rudy Giuliani -- both relatively famous when they decided to run for president -- were ahead in polls conducted in 2003 and 2007," Holland said. "Neither man won a single primary or caucus once the voting started."
A majority of Republicans are in agreement that the party should oust President Obama in 2012, with only 29 percent saying ideology is more important than electability. About 70 percent say they would prefer someone with a good chance of victory to someone they agree with on most important issues.
The poll found most Democrats expect Obama to be their candidate. About one-quarter of all those surveyed say they plan to vote for Obama, one-third say they will not vote for him and the rest are undecided.
The poll was conducted Jan. 21-23, with 1,012 adults surveyed by telephone. The group included 479 people who identified themselves as Republican or leaning to the Republicans and 441 Democrats or leaning to the party. The margin of error is 3 percentage points for questions involving the full sample.