Earlier quoted context omitted.
The Republicans have been trying to kill employer based health care forever... it's the unions responsible for it.
But they don't want to replace it with anything other than everyone buys their insurance on the open market if they want coverage, which is why unions are against it. If they wanted to move to a full coverage system (single payer?), unions would be happy because everyone has healthcare.
Citation needed.
Yes, the health care employers unions have expressed considerable interest in measures that would increase the demand for their members' services, but you're making a very different claim.