It's true that the results of the early contests have an influence on the later states. People like a winner, and they don't like a loser. Wins in the early states propel a candidate, and very poor finishes can doom a candidate. But the early states do not exercise as much power as it may appear. The reason is that collectively, early states vote pretty much the same way that later states would collectively vote if given the opportunity. The results of early contests don't simply influence the rest of the country, they also reveal how the country in general will vote.
The early states represent different regions of the country: The Midwest (Iowa), Northeast (New Hampshire), South (South Carolina), and West (Nevada). Aside from South Carolina, they are swing states. Aside from Florida, they are small enough states for most candidates to be able to compete in without needing a lot of money. If one were to switch out Iowa for another Midwestern state, or South Carolina for another Southern state, the results might be a little different, but not that much different.
To factor out any peculiarities in an early state, voters weigh results differently. Where a state is really uniquely favorable to a candidate (e.g., if a former governor of Iowa wins Iowa, or if a black candidate wins South Carolina), people give the state's result less weight. Similarly, they take results more seriously if a candidate wins on unfavorable turf. In the present primary year, South Carolina is one of the most inhospitable states in the country for Romney. That's part of the reason political observers say it's the last chance for Romney to lose: If he can win in an anti-Romney state, he's likely to sweep most of the country.
One more thought about the way early contests reveal how the later states would vote anyway, if given the chance: Imagine a deck of playing cards divided into four stacks of thirteen cards each. The "spades" stack contains mostly spades and a few clubs; the "clubs" stack is mostly clubs and a few spades; the "hearts" stack is mostly hearts and a few diamonds; the "diamonds" stack is mostly diamonds and a few hearts. One of the four stacks is selected at random and represents the winner of the contest. The first two cards of that winning stack are flipped over, revealing two diamonds. At this point, even though only two of the 13 cards have been shown, we can immediately see that "spades" and "clubs" are not going to be the winner. This is analogous to the way the early contests winnow out a few obvious losers. We can also guess that it's very likely that "diamonds" is going to be the winner, though we can't be 100% sure yet.
If the third card is flipped and also shows a diamond, it's almost guaranteed that we are dealing with the "diamonds" stack. We don't need to go down the line and turn over the 10th, 11th, 12th, and 13th cards. By the time we're just a few cards in, we know what the later cards will reveal anyway. The only situation in which we would need to see every last card in the stack is if the stack were split almost evenly, with the final card breaking the tie. For our analogy, that would be like a presidential primary where two candidates are extremely close. (For reasons beyond the scope of this post, such a situation is extremely rare. Even in 2008, where Hillary Clinton and Barack Obama fought to the end, Obama was essentially guaranteed to win months before Clinton dropped out.)
Although politically-minded individuals in the later states may wish they got to participate earlier in the primary, they can rest assured that if the order of the states was shuffled, the final outcome would be no different.
