Edwards and Clinton both need New Hampshire. If Edwards places a distant 2nd or 3rd, his campaign is basically over. If the votes are close and he wins or comes in a close 2nd, he can move on to South Carolina where it will come down to a fight between him and Obama. If Hillary loses in New Hampshire, her big selling point of electability/inevitabilty will be revealed for the house of cards it really is, leaving her incredibly vulnerable in Nevada (where Edwards' connections to labor unions keeps him relatively strong) and South Carolina (where the Dems are 50% black and will likely vote heavily for Obama or Edwards who is from SC).
Right now, Clinton leads in NH, but Obama is likely to bounce up a few points in the next few days and he could quite possibly take the top spot there, as well. Edwards is weak in NH, but he beat Clinton in Iowa and he could make it a very tight race among the top three. With Dodd and Biden withdrawing from the race, Richardson could gain some traction. The Iowa caucuses only give votes to viable candidates (those with 15% or better in each precinct) and the voters who support candidates with less than 15% have to pick a second choice among the top tier. This means that it is not only possible, but probable that Richardson's numbers are not nearly as low as they appear. He will pick up a few points against Obama and he'll get a lot of the Biden and Dodd crowd.
I'm guessing that Obama will scrape by with a win in New Hampshire, probably with 30% of the vote. Clinton will place second with 27%, Edwards will get about 20% and Richardson might hit 11-12%. If that happens, Obama wins South Carolina with 40% (possibly better), Hillary snags 30% or so, and Edwards and Richardson will get about 15% each, effectively knocking Edwards out of the race and giving Richardson a big boost in media coverage and support. As they head into Nevada, that bounce could really help Richardson who is an incredibly popular governor in the neighboring state of New Mexico. With Edwards out and Clinton looking weaker by the day, he could finish in a strong third place with 25% or more of the vote while Hillary gets into the high twenties and Obama finishes in the high thirties. And that would change everything on Super Tuesday. It's a longshot and it depends on the further implosion of the Clinton campaign and a steady weakening of the Edwards campaign, but this is how it could become a Richardson v. Obama race for the nomination. Stranger things have happened.