It’s hard to exaggerate the stakes in the first contest of the Republican nomination battle. If Trump wins there — I doubt it, but it’s possible based on current polling — he gets a head of steam into New Hampshire, where he has been performing very well. To go 2-for-2 in the initial contests would be an enormous deal, and propel him into the South, where he has also shown considerable strength, with a lot of momentum. In other words if he wins Iowa, it’s possible to see how the nomination battle becomes a desperate attempt to stop Trump by the rest of the party almost immediately.
If Carson wins Iowa (more likely than Trump prevailing there), he won’t necessarily have killed off Trump, but he will have dealt him a big blow. The same with Cruz. (Although order of finish and closeness of the results will obviously matter.) The question then will be whether Carson can make more of the bump from Iowa than Mike Huckabee or Rick Santorum were able to after their victories there.
If Cruz wins, he’s not necessarily in the same position as Trump, where you can see an early sweep. But he’d presumably get a boost into South Carolina and would instantly be at least one of the top two or three contenders for the nomination.
(Of course, given the late surges we’ve seen in Iowa, it’s possible someone besides these three wins.)
There’s been a lot of talk of how the race will eventually become Cruz v. Rubio. If the outsider-insider dynamic that has defined the race so far diminishes, it’s possible to see that, with Cruz the champion of the grass roots. But if the outsider-insider dynamic holds, it may be that it’s Trump and/or Carson against a more traditional candidate and Cruz and Rubio (among others) are competing for that traditional slot.