That's not running away from Obama.
That's continuing to try and shield Obama from any responsibility.
No, it's both. Call it 'damage control', 're-branding', or sleight of hand. Any way you look at it, it's the first step of retreat from something the Dems feel has become politically toxic.
Right now, it's just the name 'Obamacare' they're distancing themselves from. Sure, that's a naked attempt to sever His Heinous from his signature 'accomplishment' in the minds of the public, but why? It's because they've already recognized that they've unleashed something that will ultimately do great harm to the nation.
For now, they're puzzling over what to do to avoid the fallout that's headed their way. I think lots of them would vote to either make major structural changes to Obamacare, or repeal it altogether. It's already become apparent that this thing is going to end in disaster for the people, and their party, if something drastic isn't done.
Unfortunately, Big Guy is standing in the way of doing anything to fundamentally alter his glorious Socialist plan. If he doesn't soften his stance, and affirmatively communicate that he's ready to make some serious changes to this abomination, his minions are going to defect from him en masse.