In fact the opposite of your point is true. Our labor market would be more flexible if your health care was not linked to our jobs and represented and extra cost to our employer. However, considering low unemployment in the US now, I don't see this as and issue any time soon. Since US politics are basically controlled by who the middle class fear and loathe, it may be an isssue in the next recession. The middle class is doing well now, and therefore the system must be just.
Few people are worried about losing their jobs and healthcare.
So its obviously the fault of the poor that they are doing badly and therefore taxes should not be diverted to help the undeserving. Of course in a recession the middle class will not be doing as well and therefore the system must be being manipulated by the greedy rich for their own benifit. People will worry about losing their jobs and healthcare. In a recession removing the expense of health care from the workplace would also make hiring more flexible. Government healthcare may end up being the pro-business issue yet.