"Universal healthcare" is typically used as a euphemism for government-operated healthcare providers, which would wipe out both the health insurance industry and a lot of private healthcare providers. You get the strongest opposition to a policy when a specific group sees it as an existential threat, because that group will then organize to lobby vigorously against it.

Minimum wage is a price control. Price controls are trash economics and should not be used. They're a political issue in the US because a federal minimum wage is doubly counterproductive, since different states have a different cost of living. But because of that the states with a higher cost of living see a smaller deleterious effect from a higher minimum wage. Then representatives from those states can claim to want to raise the minimum wage so they can paint their opponents from the lower cost of living states as the villains when they fight against it. But nobody really wants to increase it because it's a bad policy, most of the proponents are from states whose constituents wouldn't even be affected because their state already has a minimum wage in excess of the federal one, the proponents just want to make their opponents vote it down again so they can cast aspersions over it.

A UBI is equivalent to a large universal tax credit. A slight majority of the population would receive more than they pay on net because the median income is slightly below the mean income, which creates a large base of support. If everyone voted purely in their own personal financial interest it would have simple majority support. Meanwhile most of the people who would end up paying on net would only be paying slightly (because they make slightly more than the average income), and in general the net payers are a very large diffuse group with no common interests or organizational ties to one another.

A UBI is a thereby easier to bring about than either of those other things.