First, we should define what we mean by a eugenic law or program very specifically — it can be a vague term. Usually in this context, the types of laws that were explicitly justified as "eugenic" were sterilization laws, though in some places miscegenation laws (anti "race-mixing") were justified by these terms as well. I know more about the sterilization laws than the latter, so I'm going to focus on them.

There are two categories of states for your question. The first are states that never adopted a sterilization law. The second are states that adopted a law but couldn't or didn't use it. There were several states where laws got drafted by the legislature but vetoed by the governor (the Governor of Pennsylvania vetoed a sterilization bill in 1905, saying that "It is plain that the safest and most effective method of preventing procreation would be to cut the heads off the inmates and such authority is given by the bill to this staff of scientific experts"). There were several where a law was passed by overturned by the state Supreme Court (e.g., New Jersey). As for the legal objections, any use of sterilization as a punishment for a crime, for example, goes up against the Eighth Amendment ("unusual punishment") and the Fourteenth Amendment ("equal treatment" — nobody ever suggests sterilizing white-collar criminals). In a medical context, questions of due process also come up if you are really intending of performing non-therapeutic, irreversible operations (which is to say, the operation is meant to benefit some abstract idea, like the "gene pool," not the individual being operated upon) on people against their will ("mayhem").

The legal status of such laws was extremely dicey until 1927, when the US Supreme Court ruled in Buck v. Bell that a specific form of law could be considered Constitutional. Even after that, it took effort to pass a law — there had to be some reason for it, it wasn't a "neutral" thing, and there was always strong opposition from Catholics in particular (because of the whole procreation being sacred thing). It is of note that popular eugenic appeal declined in the USA during and after the Great Depression (1929) — the idea of sterilizing the poor had less appeal when huge numbers of people found themselves poor, to oversimplify it a bit.

What's more interesting is that even among those states who passed said laws, very few of them did much with them. Here's a graph of cumulative compulsory sterilizations — you can see that one state (California) accounts for 1/3rd of them, and the rest are mostly clustered in a few specific states. This is a classic Pareto distribution, which is to say, there are some sort of systematic forces going on here that makes it very easy to use this law in some states but hard to use it in others. In a paper I published a few years back, I looked at California's case in particular — it has nothing to do with the "popularity" of eugenics or the program, it has everything to do with how the mental health system was set up and the legal framework that was enacted around it. Which doesn't answer the question for every other state, but it does point to the fact that when you are talking about turning an ideological idea (e.g. eugenics) into a practice (e.g., actual sterilization), you have to take very seriously that there are many institutions (in this case, laws and hospitals) mediating that transformation, either making it happen, or preventing it from making it happen.