When they make campaign promises, they go to small towns and talk about "Main St" businesses. Not sure why anyone believes them at this point (for the reasons you mention), but it is what they campaign on.
I think republicans could get behind some measure of portable health plans between employers. What they could not get behind is universal, in the sense of "everyone living in USA" health care footed by the US Government. The objection would be about centralization of health care funding and about, you know, who would get the benefits.