I can't stress how true this is:
Before the Affordable Care Act became the law of the land, people had two main attitudes about their health insurance. They either hated it, or they didn't use it. This idea that there were a lot of people who liked their health insurance and wanted to keep it is largely a myth. At best, the vast majority of people were afraid of change, but that doesn't mean that they thought they had great insurance or enjoyed the process of trying to get their insurer to pay their bills. In general, people hate paying for insurance and experience hassles when they try to use it. So, once the Democrats decided to push everyone into for-profit insurance, they pretty much took ownership of something most people experience negatively. Add to this that people will always want a bigger subsidy than they're getting, a bad rollout of the exchanges, and a political opposition uniformly opposed to the bill and determined to highlight every flaw within it, and you have a recipe for a political drubbing.
This is why Atrios has been saying, for a while, that love it or hate it the ACA means that the Democrats "own" everything, good or bad, that is now associated with health care.
Booman and I agree on the only correct response: mass assault on the Republican position.
The only way to make that the case is for Democrats to very thoroughly follow Ryan Cooper's advice and rally around the health care law in a relentless and single-minded way that can match the Republicans' opposition.
I have further advice on this front. The fact that formerly uninsured people are getting insurance is not a very compelling rejoinder for someone who is having a negative experience with their health insurer. What's compelling is a political party that constantly points to the benefits of the law, like annual caps, keeping your kids on your insurance, protections against having your insurance dropped, and limits on profit-taking. The way to promote this politically is to constantly talk about real people who would have been screwed without the reforms. Trot them out daily to talk about how their lives and livelihoods have been saved.
Secondly, the Dems should be introducing reforms that address areas where people are experiencing problems. These reforms won't pass, but they can form a platform of sorts that will partially inoculate the party from criticism. After all, fixing a problem is better than repealing the whole law and having a solution is more appealing than having none.
This may be counter intuitive for individual Democratic representatives who generally try to run highly individual, local, and often cowardly campaigns. Especially given that the issues that are thrown at them on the campaign trail will be a mixture of fake anti Obamacare hysteria (as in the early Fox accounts of angry people who weren't eligible for the exchanges or hadn't checked them) or real confusion and distress. If the Democrats as a party had the sense god gave a nematode they would be holding training sessions for Democrats running all over the country in saying "Yes, absolutely, let me look into that for you..." and having the Democrats as a party get out in front of the very real problems with the ACA by introducing and referencing their own fix-it bills at all times. In fact I'd be even more forward--I'd counsel Democrats to go on the offensive every minute and demand to know why the Red States are preventing people from accessing Medicaid or the Exchanges and making the population of the country sicker and weaker and why the Republicans have introduced no realistic bills to fix the health care problems their own voters face.
But this can only work if it is a co-ordinated, full frontal, assault on the Republican position. You can't expect this to be like that old joke "I was at a fight last night and a hockey game broke out." The Democrats are like herding cats, always have been. Someone is going to have to crack the whip to get them all pulling in the same direction.