Premiums did go up for some people, but those were people who had plans before that excluded certain conditions or which didn't sell to people with certain preexisting conditions. However, the Affordable Care Act has largely succeeded. It has made health insurance accessible for nearly everyone.
One reason a lot of people don't like it is that now people have associated everything that happens in healthcare with Obamacare. For instance people notice their premiums are higher the next year. They think it's because of Obamacare. But in reality premiums had been going up every year before Obamacare. After Obamacare premiums started to increase more slowly. But people irrationally blame Obamacare for the fact they are still increasing.
For people buying healthcare on their own the law limits out-of-pocket expenses, something that wasn't even in many insurance contracts before.
The idea of forcing US Citizens to purchase health insurance that they may not need or want and possibly cannot afford is government interference into personal lives. As we are in a time of economic hardship, there are many families that simply cannot afford the additional expense, and fining them is only going to make their already difficult situation harder.
The affordable car act is not always affordable. People all have various incomes and different bills that need to be met, so in today's society the most affordable thing is anything that is free. People are struggling and having a hard time so anything that costs a good amount of money isn't affordable.