WASHINGTON (CNN) -- We're seeing a split-level campaign. The national campaign is mostly about celebrity. Hillary Clinton is the best-known contender. She has a solid lead among Democrats nationally, where she leads runner-up Barack Obama 46 to 23 percent in a new CNN/Opinion Research Corporation Poll.
Mitt Romney is is leading the race for the Republican presidential nomination in Iowa and New Hampshire.
But where there's a campaign, like in the early voting states, things look different.
A new Los Angeles Times-Bloomberg poll in Iowa shows a close race among Clinton (28 percent), John Edwards (23 percent) and Barack Obama (19 percent).
The poll also shows Clinton leading in New Hampshire and South Carolina, but by margins smaller than her national margin.
The Los Angeles Times/Bloomberg poll had a margin of error of plus or minus 5 percentage points.
If Clinton's rivals are going to stop her, they're going to have to do it in the early states. Then, the national polls could suddenly change, as they did in 2004 after John Kerry beat Howard Dean in Iowa and New Hampshire.
Rudy Giuliani's the national Republican frontrunner, with Fred Thompson breathing down his neck.
Giuliani became a celebrity after 9/11. Thompson's a TV celebrity.
But the GOP frontrunner in Iowa and New Hampshire, former Massachusetts Gov. Mitt Romney, is the candidate who's running fourth in the national polls.
"I'm encouraged that, in the states where I spend the most time like Iowa and New Hampshire, I am doing best," Romney said.
Where there's a campaign, things look different. In South Carolina, Thompson's slightly ahead, leading Giuliani 26 percent to 23 percent. South Carolina voters may recognize Thompson's Southern accent.
"It's good to be in a place where I know that when I talk, people can understand what I'm saying," Thompson said in the Palmetto State.
Where there hasn't been much of a local campaign, things look pretty much the same as they do nationally, such as in Florida, which has scheduled an early primary. A new Quinnipiac poll shows the national frontrunners, Clinton and Giuliani, leading comfortably in Florida.
All the major Democratic candidates have signed a pledge not to campaign in Florida because its early primary violates party rules. That's good news for Clinton. If there's no local campaign, the national frontrunner is likely to win. E-mail to a friend
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