I've had a few interactions with Clinton supporters over the past few days. Some went better than others, but all were rather tense. I've been on the losing end of enough campaigns to know how much that stings, but this one is unusual, partially because of how close it was.
In terms of pledged (elected) delegates, Obama beat Clinton 1765.5 to 1639.5. Every contest mattered, as did the superdelegates. This was the closest presidential nominating contest we've seen since the current system of primaries and caucuses was created in the early 1970s. Another way of saying that is that no winner has ever come so close to being the loser, and no loser has ever come so close to being the winner.
On top of that, the Clinton folks have plenty to be bitter about. She really did get some crappy and misogynistic coverage in the media, and not just from Chris Matthews. I heard a number of people I respect, including several women, say that they didn't like her because she seemed too "ambitious," which is one of those ridiculous anti-feminist code words. (Just to be clear: Hillary Clinton is ambitious. Barack Obama is ambitious. So's John McCain, John Edwards, and pretty much everyone who's ever thought about becoming president.) This isn't to say the press has been easy on Obama. They were for a while, until he became the frontrunner, and then came all the crap about Rev. Wright and flagpins and attending a madrassa, etc. But the media didn't do Hillary any favors.
(A number of Clinton folks have mentioned to me that they're also upset about Obama not winning the "popular vote." I really, really wish the Clinton campaign hadn't used that argument. Not only was it disingenuous, but it had the particularly pernicious effect of undermining the legitimacy of Obama's nomination. But the belief persists and it's sincerely held.)
All this is to say that the Clinton folks are upset, they're hurting, and they're going through various stages of loss. Give them space, give them time, maybe offer a kind word. The party's had worse divisions before. This one will heal. But not overnight.