In a comment, Spencer wrote,
You just can not resist claiming that firms were required to provide health insurance.
It may not matter whether you think of firms as obligated to provide health insurance or as incentivized to provide it. The trend toward reducing the number of full-time workers would be affected by rising health care spending nonetheless.
Workers differ in their preferences for employer-provided health insurance and take-home pay. This leads to clientele effects. That is, workers who place a high value on employer-provided health insurance will seek to be full-time employees. Workers who would rather receive more take-home pay and deal with health insurance some other way will instead prefer to be hired as contractors.
As health care spending rises, these clientele effects get stronger. One would expect to see more workers noticing that they can get higher take-home pay as contractors, and one would expect to see firms notice that their compensation costs for hiring contractors are coming down relative to the cost of hiring full-time workers.