As "shelter in place" or "stay at home" orders expand to more states (and can be expected to expand further), it's useful to make a distinction between "stay at home" measures and the more extreme step that has, except in a handful of cases, not yet happened: quarantine.
The rules for stay-at-home social distancing vary by state and county, but the general outlines are this: Residents are allowed to leave their home for essentials, like grocery shopping and required doctor visits. They are asked not to leave home for nonessential activities, like eating at a restaurant or going to a local bar. Those businesses are either closed or reduced to takeout-only. Getting a haircut, shopping for clothes, going to a theater, even routine dental cleanings—no.
It's devastating to small businesses, and it’s the reason Congress has been scrambling to provide at least some relief to service-sector workers who have either already been laid off or may soon be. But it's still less draconian than that other potential step: quarantine.
Poynter has a brief summary of state and federal quarantine laws. The government does, in a public health emergency, have the legal authority to bar Americans from leaving their homes or hospital rooms period, a step that has been reserved to isolate individuals with especially dangerous, especially infectious diseases. (Note, too, that we're not talking about the isolation regularly done in hospitals when dealing with potentially transmissible diseases—those measures are intended to protect workers and other patients, but are a far cry from a legal order requiring an individual to stay in isolation on pain of imprisonment.)
Those legal orders are extremely unlikely to become widespread in the current case, simply because we've already lost control of the virus in question. Due in large part to an inability to track the virus in its early days, it is now widespread enough that extreme isolation of known individuals wouldn't put a dent in the total infected population.
By the time those who are infected are sick enough to seek medical attention, they have already been spreading the virus for days; many will never be sick enough to seek medical attention before getting better, and will never be identified as carriers.
If we had near-universal testing capabilities, quarantine might have been the tool used instead of our current stay-at-home orders. We could isolate only the individuals who have tested positive, and might even choose to do so on penalty of fine or jail time, while leaving the rest of the economy open for business.
Similarly, if the virus was concentrated only in easily identified "hot spots" around the country, for example in Washington state and in New York City, the imposition of regional quarantines prohibiting nonessential travel to and from those regions might have been an available tool, as it was in Wuhan, China.
It's draconian, and Americans would be furious at such measures—but it is moot, because the virus has jumped from numerous original landing points, known and unknown, and is now nationwide. Limiting travel is no longer a useful tool, draconian or not.
Social distancing, on the other hand, is precisely the tool needed for the emergency we have now been forced into. Vigorous cleaning, hand-washing, and staying out of virus-shedding range of others whether you or they are known to be infected or not eliminates transmission. The virus runs its course in those infected without ever having the opportunity to infect others, aside from other members of the same household.
It is intended to buy time until a vaccine is available, but mostly it is intended to slow the transmission as much as possible so that severely ill patients are "spread out" over months, rather than weeks. It is intended to keep patients from being denied care in overfilled hospitals, as is happening right now, as we speak, in Italy.
Stay at home orders are likely to be necessary at least until U.S. testing efforts can become widespread, giving us the chance to successfully isolate (or, yes, “quarantine”) only affected individuals. Until that day, preventative “social distancing” is the only tool available.
All that said, there may be one way the spread of the virus could change in a manner that would require larger "quarantines" of the sort enforced by armed law enforcement officers or National Guard troops. There is currently a public debate among elected lawmakers about whether the "cure" of social distancing is so high an economic price to pay that restrictions should be reversed and the virus simply be allowed to take its course, killing whatever percentage of Americans it will kill but letting the economy more quickly get "back to normal." This will not work, because piled bodies themselves represent a considerable economic drain, but regardless—it is being seriously proposed by some.
Specifically, it is being proposed by Republican lawmakers in Republican-held states, while Democratic-held states tend to be holding firm on the need for social distancing measures. If the two sides were to truly split, with the virus becoming intentionally unchecked in red states while blue states maintain enforcement measures, the notion of travel restrictions between the two suddenly seems more plausible. Not a full quarantine of outbreak-spreading states, but travel restrictions? A possibility.