Most liberals would prefer to take insurance companies out of the picture altogether and just have government pay health expenses directly. While the right has made "Obamacare" the preeminent cause to attack, this health care plan is actually the conservative plan, circa 1993. It's what the Republican Congress countered "Clintoncare" with and it came directly out of a right-wing think tank, the Heritage Foundation. That's why Mitt Romney took it and implemented it in Massachusetts--because, at the time, it was considered a right-wing, market-based solution. He never dreamed that it would eventually be used as an example of how left-wing he was.
Obamacare, when it was implemented, was basically a partial step towards what liberals actually wanted, not the end point. Starting the process towards persuading the American people that access to health care is an necessary thing for government to assure everyone was important, even if the bill that was passed was imperfect. So that's why Democrats and liberals tend to support it, while not necessarily liking insurance companies.