Just to clarify the above post... since the volume of alcohol is the trigger, and most red wines are on average 14% alcohol by volume... you actually have to bring in a large amount of wine to get your potential total customs bill to a figure that warrats the officers to want to write you up.

Its a different thing when you bring in spirits.... hard booze will have about 40% alcohol (some high octane stuff up to 50%) alcohol and its there that Uncle Sam starts to collect $$$ quickly.

In my experience with wines and US Customs, you can even bring in 3 cases (36 bottles) of red wine and as long as you declare it, chances of getting written up and charged duty is less than 5%.