First of all, whatever finally makes it out of committee will probably be named after Kennedy. Which is, instantly, much better branding. The Democrats have been bad at this since forever. Clinton's health care package is still called "Hillarycare." This is occasionally being called "Obamacare," which is an improvement. But "Kennedycare" has a much nicer ring to it. From a ball-busting non-stay-at-home wife to a scary Muslim black man to drunk Irish Catholic American royalty—the bill is getting progressively less scary to easily frightened white people.
Noam Scheiber has raised the point that a week or two of nonstop, mostly positive Kennedy coverage is, by proxy, nonstop, mostly positive health care reform coverage. At the very least, it distracts from the messy "what secrets does the bill hold" and "what is the current political status of the bill" coverage and turns it back into a historic opportunity to do things we've been trying to do for generations.
Scheiber also argues that Kennedy's death makes a filibuster less likely. It would be particularly craven to filibuster when the Democrats can't vote for cloture because their party's most respected legislator just died. And, if nonstop positive Kennedy coverage does crowd out nonstop Town Hall Wacko Death Panel coverage (and frankly that was mostly just a very effective news-free August political distraction anyway) public opinion may shift again, the actual popularity of nearly all the reforms in the bill may actually get reported on, and it would suddenly be less politically popular to be obstructionist.
But all of this is a big maybe!
Because as we've seen, Republicans are craven opportunists more concerned with scoring political points and spreading misinformation than actually ever doing anything good for anyone. During Kennedy's absence from the Hill, some have already claimed they would be working toward an acceptable compromise if only Ted was around. There's no reason to think they won't mourn Kennedy's death by complaining that the surviving Democrats in the Senate are so much less willing to reach across party lines.
And they could try to make this another Wellstone Funeral moment.
When liberal Senate hero Paul Wellstone died, Democrats used his memorial service as an opportunity to advocate for advocate for the causes he devoted his life to. This was called "politicizing" his death, and Every Serious Person in journalism agreed that it was positively disgusting. Sure, it might honor Paul Wellstone's memory to fight for social justice and promote Democratic policies, but it is very Rude and Improper to say you are going to do that.
The media environment is quite different now, and attempts to argue that it "politicizes" Kennedy's death to promote health care reform in his name might not get the same agreeable coverage now that it did then. But it's still a very real possibility.
Finally, there is the inescapable fact that Ted Kennedy's death means one less vote for health care reform. Maybe Massachusetts will allow Deval Patrick to appoint a placeholder Senator. Maybe. Or maybe the Democrats will still have 58-and-a-half senators, making a filibuster unbreakable, especially with useless and unreliable "Democrats" like Kent Conrad.