Washington (CNN) -- His party got its clock cleaned in Tuesday's midterm elections, but President Barack Obama still remains competitive in some hypothetical 2012 presidential election matchups, especially against Sarah Palin, a new poll shows.

A CNN/Opinion Research Corp. survey released Thursday also indicates that at the unofficial start of the race for the Republican presidential nomination, the field of possible contenders appears wide open with no front-runner.

Twenty-one percent of Republicans say they would most likely support 2008 GOP White House candidate and former Arkansas Gov. Mike Huckabee for their party's 2012 presidential nomination, according to the poll.

The number is 20 percent for another 2008 Republican presidential hopeful, former Massachusetts Gov. Mitt Romney.

Fourteen percent say they support Palin, the former Alaska governor and 2008 GOP vice presidential nominee, with 12 percent backing former House Speaker Newt Gingrich of Georgia.

The remaining candidates, whose names were all in single digits, are led by Rep. Ron Paul of Texas, who also ran for the GOP presidential nomination the last time around, followed by Mississippi Gov. Haley Barbour, Minnesota Gov. Tim Pawlenty, Rep. Mike Pence of Indiana, and former Sen. Rick Santorum of Pennsylvania.

The poll's release comes as Santorum visits New Hampshire to give a speech about the midterm election results and the future of the Republican party. No one has yet to announce a bid for the GOP nomination.

In a possible general election showdown, Obama leads Palin 52-44 percent among all registered voters.

"Looking ahead to 2012, it may be too early to count Barack Obama out, particularly if Sarah Palin is his opponent," said CNN Polling Director Keating Holland. "The former Alaska governor gets a lot of attention, but she is in third place when Republicans are asked to pick a presidential nominee, and in a hypothetical matchup with Obama she is arguably the weakest candidate of the top-tier GOP hopefuls."

In a hypothetical 2012 matchup, Huckabee leads Obama 52 - 44 percent, while Romney has a 50-45 point advantage, which is within the poll's sampling error. Obama holds a 49-47 percent margin over Gingrich.

The poll indicates that four in 10 have a favorable opinion of Palin, with nearly half saying they have an unfavorable view.

Romney has a 36 percent favorable rating and a 29 percent unfavorable rating, with 35 percent unsure.

Forty-two percent say they see Huckabee in a positive light, with 26 percent saying they hold a negative view and just over three in 10 are unsure.

Gingrich has 32 percent favorable rating, with four in 10 saying they have an unfavorable view, and 28 percent unsure.

On the Democratic side, nearly three-quarters of Democrats say they want to see the party renominate Obama in 2012.

Why does that matter?

"No incumbent president has faced a significant primary challenge and gone on to win re-election in November, Holland added. "Contested primaries make incumbents look weak and overly-political, and prevent the incumbent from building up goodwill while the opposition party candidates are fighting among themselves."

Avoiding a primary challenge won't guarantee Obama victory in November 2012, but the fact that 73 percent of Democrats want to see the party renominate Obama may scare off any Democrats who are contemplating a run against him, and that gets him one step closer to a second term.

The poll of 1,006 adult Americans, of which 921 were registered voters, was conducted by phone October 27-30, before the midterm elections.

The sample also included 500 respondents who describe themselves as Republicans or independents who lean Republican, and 453 respondents who describe themselves as Democrats or independents who lean Democratic. The survey's overall sampling error is plus or minus 3 percentage points.

CNN also conducted exit polls on Election Day in some of the states that vote first in the presidential primary calendar.

In Iowa, 21 percent of Republicans questioned as they exited the voting booth said that Romney was their likely choice in the 2012 Iowa caucuses, with Huckabee also at 21 percent, Palin at 18 percent, Gingrich at 7 percent and one in five saying they would support another possible candidate.

In New Hampshire, 39 percent of Republicans said that Romney is their likely choice in the state's primary, with Palin at 18 percent, Huckabee at 11 percent, Gingrich at eight percent and 19 percent saying they would back another possible contender.

Twenty-five percent of South Carolina Republicans say Palin would be their likely primary choice, followed by Huckabee at 24 percent, Romney at 21 percent and Gingrich at 10 percent.

CNN Deputy Political Director Paul Steinhauser contributed to this report.