All the polling and analysis of the 2008 presidential primaries neatly bifurcate their consideration into partisan categories. In the Democratic primary, Clinton, Obama and Edwards face off, while in the Republican contest, the polls take measure of Giuliani, McCain, Romney and, depending on their assumptions, Gingrich and Fred Thompson.

But this analysis fundamentally ignores one of the most important elements in the looming contest of 2008: the likelihood that independents and even Republicans may enter the Democratic primary to support or oppose Hillary Clinton. So polarizing is her candidacy that the migration into the Democratic primary could be enormous, even so large as to overshadow the core Democratic partisans who always vote in their party’s contests.

In all, 24 states — including big ones like California, Texas, Ohio, Michigan, and Illinois — with a combined 56 percent of America’s population permit independents to vote in the Democratic primary; 19 states, with 39 percent of the population, let anyone vote in either primary, even if they are registered in the opposite party. More importantly, among the early states, Iowa, New Hampshire, and South Carolina have completely open primaries and permit voters to choose whichever primary they wish.

California law is particularly odd (as is often the case with that state). Independents can vote only in the Democratic primary — not in the Republican contest. This provision virtually assures a massive influx of unaffiliated voters into the Clinton-Obama battle.

Crossovers were an important factor the last time both parties had simultaneous nominating processes. In 2000, Bush and Gore wrapped up most of the votes of the loyalists of their respective parties while challengers McCain and Bradley split the independent vote. Had either McCain or Bradley not run, it is possible that the remaining candidate would have gotten so many independent votes that he might have been nominated.

But in 2008, all the gravitational pull will be into the Democratic primary. If Giuliani is well ahead by primary season, the GOP contest could turn out to be anti-climactic. But even if the Republican primary will be fought closely, none of the candidates has the same potential to attract or repel voters as Hillary Clinton.

So which will it be? Will Hillary attract or repel independent voters? The Gallup organization recently released a composite of its polling on Hillary among independents over the past three years. It found that while Democrats hold a favorable opinion of the former first lady by 83 percent to 13, independents break in her favor by only 51 percent to 43. Republicans, needless to say, dislike her: Among GOPers the favorable rating is only 20 percent to 76.

Given these data, two factors would indicate that the crossover voting laws may spell trouble for Hillary:

If she only leads Obama by 5 to 10 points among Democrats when she has an 83-13 favorability rating, she will likely do much worse among independents.

The passion and the depth of animus against Hillary, particularly among Republicans and Republican-leaning independents, may be so intense as to motivate them to participate in the Democratic primary in great numbers.

Most current polling fails to capture the likelihood of crossover voting. News media surveys generally ask Democrats what they think about the Democratic field and Republicans what they think about the GOP contenders. Since half the states do not permit independents, much less members of the opposite party, to enter the primaries, few national samples ask independents what they are likely to do.

Those that do tend not to divide their samples along the lines of each state’s law; fewer still ask Republicans if they will vote in the Democratic primary. So crossover voting is a blind spot in most current polling.

All strategists and pollsters need to amend their thinking to view the primaries as the three-dimensional processes they really are.