You are entitled to 1 litre of wine duty free per person traveling together. Above that you may have to pay duty. That said, wide experience is that CBP will not assess duty on bottles over the limit so long as it’s for personal use. (My recent personal experience was 6 bottles with no questions at all once I declared). That said, from a quick read of the links in that link above, the duty rate is 7c/gallon, so no wonder they don’t bother charging it. A case would be about 14c (net of the first litre “free”).
There’s a separate question about what the airline will accept, and that may vary by airline.
This is not entirely true.
You are entitled to one liter of alcohol, not one liter of wine.
Assume your bottle is 13.5% alcohol. That leaves you with .865 liter that you can still bring in. It is more complicated if one bottle is 12.5 and one is 14 and another 13.8.
Because many people in US customs are proud graduates of the US education system, most of them can’t figure out where your liter ends and what the tax would be.
That ends up benefiting you, the traveler.
FWIW, I’ve brought in many cases of wine with no problem.
Separately Andrew is dead on about what the airline will accept. Each terminal in the US tends to be dominated by one airline and they will establish their own rules. A second set of rules will be in place for each airline using that terminal. A third set of rules will be in place for the people working that particular shift at that particular airport.
How does this translate into action?
As follows.
The airline might let you ship in a cardboard box. They may require styro containers within the box.
The airline or airport may have some other hoops you need to go through to get a cardboard box shipped, e.g. they may want you to check it at one particular place, etc.
The people working that shift at that airport might say that they won’t accept cardboard boxes. Whether this is company policy or not doesn’t matter in the least. You will miss your plane.
I travel several times a year with cardboard boxes of wine and most of the time, like 99% of the time, if the wine is packed in styro and labeled “fragile”, it’s OK. But on occasion, I’ve had serious arguments with the check-in staff regarding cardboard boxes. So the best idea is to arrive early.