Washington (CNN) - Call it a sign of how unsettled the GOP presidential field remains: Two of the three people at the top of new national poll in the battle for the Republican nomination may not even run for the White House. And a CNN/Opinion Research Corporation survey also suggests that there is not a lot of enthusiasm about any of the major candidates.
According to the poll, which was released Friday, 16 percent of Republicans and independents who lean towards the GOP say they would most likely support Rudy Giuliani as their party's nominee. One point behind, at 15 percent is Mitt Romney, with Sarah Palin coming in at 13 percent.
Full results (pdf)
Romney, the former Massachusetts governor and 2008 GOP White House hopeful, will officially announce his candidacy for president next Thursday. Neither Palin nor Giuliani have taken concrete steps toward a run.
Palin, the former Alaska governor and 2008 Republican vice presidential nominee, has increasingly sent signals that she is interested in running. On Sunday she kicks off a campaign-style bus tour, but she has not publicly worked toward hiring staff or building an organization in any of the early voting states in the primary and caucus calendar.
Giuliani, who was a candidate in the last presidential cycle, is also considering another bid, but an adviser tells CNN that the former New York City mayor is not taking active steps toward getting in the race other than making recent appearances in New Hampshire, which holds the first primary on the road to the White House.
"Giuliani has the top spot in a 12-candidate field, but he doesn't generate a lot of enthusiasm. Only about a quarter of Republicans nationwide said that they would be enthusiastic if Giuliani won the nomination," said CNN Polling Director Keating Holland. "But he's not alone - only a quarter would be enthusiastic if Palin got the party's nod, and only one in five would feel the same way if Romney became the GOP's standard bearer in 2012."
Just one point behind Palin in the survey is Rep. Ron Paul of Texas, who is making his third bid for the presidency. With a sampling error of plus or minus 4.5 percentage points, the poll indicates a crowded field at the top of the horse race.
Former Godfather's Pizza CEO and radio talk show host Herman Cain is at ten percent, with Former House Speaker Newt Gingrich at eight percent, Rep. Michele Bachmann of Minnesota at seven percent and former Minnesota Gov. Tim Pawlenty at five percent. Everyone else questioned registered at two percent or less.
The survey was conducted May 24 through May 26, after former Arkansas governor and 2008 Republican presidential candidate Mike Huckabee, billionaire businessman, real estate mogul and reality TV star Donald Trump and Indiana Gov. Mitch Daniels all announced they would not make presidential bids.
With Giuliani out of the race, Romney takes in the top spot at 19 percent with Palin close behind at 15 percent. And with Palin and Giuliani out of the running, Romney's share of the vote increases to 21 percent, with Paul at 15 percent.
"Romney, Giuliani and Paul have a reservoir of goodwill among Republican voters, but Gingrich and Palin are more polarizing figures," Holland noted. "More than six in ten Republicans have a positive reaction to the idea of Romney, Giuliani or Paul winning the nomination. But nearly half say they would be displeased or upset if Gingrich won the party's nod in 2012, and more than four in ten Republicans feel the same way about Palin."
The poll indicates six in ten GOPers say they are satisfied with the field of GOP candidates, but only 16 percent say they are very satisfied.
Are they looking for a new hat in the ring?
Maybe, but a majority give a thumbs-down to a presidential bid from either Texas Gov. Rick Perry or former Florida Gov. Jeb Bush, who have both said they are not interested in running for next year's nomination. The survey indicates Republicans are divided on whether they'd like to see New Jersey Gov. Chris Christie or House Budget Chairman Rep. Paul Ryan of Wisconsin run for the nomination. Both Christie and Ryan have also declared they are not making bids for the White House.
– CNN Deputy Political Director Paul Steinhauser contributed to this report
– Follow Paul Steinhauser on Twitter: @PsteinhauserCNN