Former New York mayor Rudy Giuliani said last week on CNBC that he is "absolutely" open to considering another presidential run in 2012. That tells you all you need to know about the fluidity of the GOP's coming nomination contest.

Not that Giuliani is likely to be a serious candidate. The odds are low that he'll even run. Given the ineptitude of his 2008 candidacy and his relatively liberal views on abortion and gay rights in a party that, if anything, has become even more conservative in recent years, it's difficult to see a path to the nomination for him. But with the field so unsettled, anybody can dream.

Giuliani isn't the only long-shot Republican whose musings about a possible 2012 run underscore the challenge facing party activists, strategists and elected officials trying to divine the likely nominee. Over the Christmas holiday, Jon Huntsman, the U.S. ambassador to China and a former governor of Utah, suggested to a Newsweek reporter that he might consider running in 2012.

President Obama couldn't resist poking fun at that notion during last week's news conference with Chinese President Hu Jintao. With Huntsman sitting in the front row, Obama was asked about a possible challenge from his ambassador. Obama was clearly ready for the question. Praising Huntsman's work, he said with a grin, "I'm sure that him having worked so well with me will be a great asset in any Republican primary."

Republicans' confusion about their presidential nomination contest runs deep: They are confused about who may actually run and about who might be their strongest candidate against an incumbent president who looks more formidable today than he did just three months ago.

Excluding a handful of almost certain candidates - including former Massachusetts governor Mitt Romney, former Minnesota governor Tim Pawlenty, former House speaker Newt Gingrich and former Pennsylvania senator Rick Santorum - the Republican field is full of question marks.

The list of possibilities starts with the Republican who attracts more attention than almost everyone else combined, former Alaska governor Sarah Palin. Beyond Palin, however, there are former Arkansas governor Mike Huckabee, Mississippi Gov. Haley Barbour, Indiana Gov. Mitch Daniels, South Dakota Sen. John Thune, Indiana Rep. Mike Pence and perhaps a few others. Businessman Herman Cain has formed an exploratory committee. And there are also those who have said no but who still generate speculation, including New Jersey Gov. Chris Christie and Texas Gov. Rick Perry.

National polls offer little guidance on the likely nominee's identity, although they are heavily reported and closely analyzed for clues. The latest Washington Post-ABC News survey put the pecking order this way: Huckabee, Palin and Romney bunched between 20 percent and 16 percent among registered Republican voters, with Gingrich fourth at 10 percent. The latest NBC News-Wall Street Journal poll showed the order as follows: Romney, Huckabee, Palin and Gingrich, with their numbers almost identical to those of the Post-ABC News poll.

Republican presidential nomination campaigns often devolve into a contest between the party's establishment wing and its conservative or insurgent wing (although the establishment wing today is not to be mistaken for moderate). Other observers describe the contest as pitting the Fox News contingent (Palin, Huckabee, Gingrich and Santorum are all on the TV channel's payroll) against the rest of the field. Given what happened in the 2010 primaries, the 2012 race could be establishment vs. tea party, although everyone running will find ways to present themselves as in tune with the tea party.

National Journal's Ron Brownstein, a shrewd analyst of coalitions and demographics, describes the coming GOP race as a variation on the establishment vs. conservative theme. He calls it managers vs. populists. Romney epitomizes the managers, along with people such as Daniels and Barbour. Palin and Huckabee are the prime examples of the populists. Gingrich, Pawlenty and Thune fall somewhere in between.

The Republican Party may be more ideologically homogenous than it's been in the past, but there are clear fissures that will shape the nomination campaign. The Post-ABC News poll showed significant divisions along income lines. Palin and Huckabee were disproportionately popular among white voters with household incomes below $50,000, while Romney did disproportionately better among those with incomes above $50,000. The same held true for education: Palin and Huckabee were even more popular with Republicans who lack a college degree, Romney even more popular among college graduates.

Voters with household incomes above $50,000 made up a significant portion of the electorate in the early primaries and caucuses in 2008. In Iowa, they accounted for 63 percent of voters, in New Hampshire 76 percent and in South Carolina 72 percent. That would seem to be good for Romney, though three years ago he lost all three of those states. The other reality is that the Republican Party has attracted more downscale voters in recent years.

By next fall, state polls will be a far better indicator than national polls of the shape of the Republican contest. (Four years ago, Giuliani led national polls of Republicans.) Today, Huckabee leads among Republicans in Iowa, while Romney has a substantial lead in New Hampshire, his most critical state. In South Carolina, which has a history of deciding the GOP nomination, a poll taken last fall showed no clear leader.

In past Republican races, there has almost always been a candidate to beat: George H.W. Bush in 1988, Bob Dole in 1996, George W. Bush in 2000, John McCain in 2008. All faced adversity along the way, but all still won. (McCain was given up for dead politically halfway through 2007 but managed to prevail.)

Ask Republicans who that candidate is for 2012, and many will say Romney. Why? Because he's run before, can present himself as an economic manager, will have plenty of money and roughly fits the profile of previous GOP nominees. Not because he is a commanding front runner - the polls clearly show otherwise - or without negatives (think Massachusetts health care). And not because he is the darling of the hard-core conservatives who are energizing the GOP more than ever.

The Republican race is starting slowly for the very reason that it is so full of uncertainty, with more questions than answers about the field. What that means, for now, is that everyone can be a dreamer.