Yes, I believe it is here to stay. The law passed in both the Senate and Congress and the Supreme Court upheld it.
Having said that most people who have a job will continue to get insurance through their employer.
Personally speaking it has not effected me or anyone in my circle. The hardship however is for people who are unemployed, self-employed, or do not work for a company which offers health insurance as a benefit.
People resent being (forced by the government) to get insurance or anything for that matter! In California I remember the fight over being forced to have auto insurance, wear seat belts, and also a helmet when riding a motorcycle.
Banning smoking in all public buildings including restaurants and nightclubs was seen as government over-reach. Several years ago when the government added fluoride to drinking water that upset a lot of folks! However after awhile all these laws became a way of life.
When FDR pushed for Social Security and Medicare a lot of people were angry about having money taken out of their payroll checks against their will. Today Social Security and Medicare are considered "sacred cows". No presidential candidate could get elected if one of his/her goals were to abolish either of them. Projections for 2016 indicate Obamacare will have at least 22 million signed up. The more people who have it the more difficult it will become to eliminate it. Overtime it will become the "norm" just like Social Security.