When a tax is hidden like this it doesn’t appear like a tax and people can’t effectively object to it but the dissatisfaction with the program speaks to the fact that just concealing a problem like this doesn’t get rid of it.
Costs
However, the far larger problem is that the United States ranks toward the top in terms of per-capita medical expenses but near the bottom in terms of quality of coverage. It is very much like we are paying for brand new Rolls Royce quality service but actually getting used Yugo, which isn’t sustainable. If you have a cost vs. service problem you need to address this first but instead both parties are largely focused with moving these unaffordable costs around to different groups of people who understandably don’t want to pay them. If either party truly wanted this to work and assure they would be reelected a focus on eliminating these extreme costs would seem to be the more intelligent path but, instead, both groups seem to be focused on sticking these costs to the demographic that typically votes for the rival group.