- Those who earn less than 100% of the federal poverty level ($12k/year for an individual, $25k/year for a family of 4) in states that haven't expanded Medicaid (~2.2 million people [0])
- Those who earn more than 400% of the federal poverty level ($48k/year for an individual, $100k/year for a family of 4) but aren't offered health insurance through an employer (e.g., because they're self-employed or work for a small business) (~900 thousand people [1])
Both are legitimate and significant coverage gaps, but they only affect ~1.5% of non-elderly adults in the US. For comparison, the number of adults that qualify for free or subsidized coverage but chose not to enroll is about 4x larger as of 2016 [2].
[0] https://www.kff.org/medicaid/issue-brief/the-coverage-gap-un...
[1] https://www.commonwealthfund.org/publications/issue-briefs/2...
[2] https://www.kff.org/uninsured/issue-brief/estimates-of-eligi...
By contrast, Medicaid in the United States is administered to the states, who have broad leeway in determining who is and who is not eligible for the system, especially after National Federation of Independent Business v. Sebelius. Income level alone does not necessarily qualify one for Medicaid. Medicaid is not considered universal health care, even with the ACA, and that makes a huge difference.
It's not so much that Americans don't want the Swiss system as that we're missing the crucial part of the Swiss system that makes people feel secure that they'll be insured.