You would not see costs going down.
Health care costs don't go down. What you would see and DID see (I know from being alive the last few years) is that in states where it was enacted as designed those rates of increases were less than A) states that failed to do that and B) lower rate of increase than prior to the bill.
https://www.theatlantic.com/health/archive/2013/11/the-state-where-obamacare-is-working/281411/
http://www.slate.com/articles/business/moneybox/2016/08/is_obamacare_doomed_all_your_questions_answered.html
http://www.huffingtonpost.com/2014/08/05/states-obamacare_n_5650606.html
http://time.com/money/4209465/is-obamacare-working/
http://www.nationalmemo.com/obamacare-working-states-arent-sabotaging/
Again, it is hard to keep a 'promise' if the ground keeps shifting. I promise I will wash your car. I get your car all soaped up and the utility led by a govt that wanted to see my promise unfulfilled cuts off my water supply. You charge that I failed in keeping my promise to wash AND rinse your car. Kinda hard to do if the ground shifts.