In the US? States' rights. Those who are against the PPACA, for example, are primarily against a [i]federal[/i] healthcare mandate. Individual states, however, can do as they please (see: Massachusetts). Look at other controversial issues in politics today. Gun laws, marijuana legalization, gay marriage, different states have different laws with respect to those issues. But even the most anti-whatever activists don't say states shouldn't have the [i]right[/i] to enact those laws. Being against mandates coming from a federal level doesn't have to mean you're taking a stand on the issue itself; you just have a fundamental problem with the federal government doing what you think should be left to states.
In general, Americans favor a federal government that minds its own damn business thank you very much*. States should be able to handle their own affairs, while the federal government, which unites the states of America, deals with ensuring their prosperity in terms of dealing with other nations. The times when people actually like mandates that come from Washington are few and far between. If Biden announces a federal ban on assault weapons or high-capacity magazines, at least some hell is going to break loose.
*Also the reason why the idea of paying more in federal taxes isn't too desirable; if people wanted the federal government to be more active, they would be willing to fund it.
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pretty much this.