Obama’s loss would have been easier to swallow for his supporters, I think. He’s young, he’s new, he would have a realistic second shot, many of his supporters have not been political for that long, etc.
In contrast, Hillary has been a standard bearer for many people (women of course included) a long while. People have been looking forward to this run in some ways since she was in the White House with Bill. The idea was always there for many of her supporters that Hillary would be the one to break the gender barrier in presidential politics. It’s been a long time coming and now it will be hard to let go.
I don’t doubt that some older women I know will never vote for Obama because he’s in the unfortunate position of having won this election, this extremely important, symbolic election for them. These are not issues voters, these are women who feel that a woman has been wronged. Therefore issues arguments will not appeal to them- they must be assuaged by the candidate herself, a celebration of Hillary in the press, things that are already happening to a degree. Obama is the interloper, he’s jumped the gun, he was in the way, he was installed by the system/media- I think all of these complaints are more important than racism in the backlash against Obama.
Over the next few months, however, without constant reinforcement from Hillary, and in fact with her working against it, the echo chamber will lose some of its integrity, and folks will trickle out, leaving a higher density of extreme folks, which will cause more to trickle out. In my opinion, Obama and his staff* have largely been very respectful of Hillary and her supporters, and this will reflect in the success he will have with people who polled Hillary.
For most of them, in the end, Obama will be the lesser of two evils, which is a position we are all familiar with.
*edited- originally I had “Obama and his supporters” here, which is unfortunately incorrect- there has been a lot of vitriol towards Clinton and her supporters from Obama supporters (myself included). But the campaign has been very careful to be noble and has largely succeeded in my view.