It is possible, but it is a long and expensive process. Any plants shipped from oversees to the US has to go through a USDA inspection and quarantine process, depending on where you ship it from. It would be best to contact USDA well ahead of your travel time and enquire about the regulations, requirements, procedures and costs to give you a better sense. Please, don't try to somehow bypass the process, because you will get caught, all your plants will be destroyed and you could face a hefty fine and/or jail time. Not to mention the danger that comes from inadvertently introducing new pests, weeds or diseases and bugs to North America.
Hope that helps. And good luck!

I did all of the above, taking with me a list of plants not allowed to be brought into the US when I went to a Gardening Course in England. They also had the list. It was at Great Dixter Gardens, and they were very familiar with sending people back with plants as they had been doing this course for years. Anyway, I bought my plants - sans dirt - you cannot bring in any form of dirt so you'll have to take cuttings -- and flew into the US WITH all the proper forms and inspection paperwork already made out. It didn't seem to matter. They held me up for 14 hours (I missed my plane, had to stay overnight) until a "special inspector" arrived, and by the time he finished, he'd thrown out half my plants! Boy were those expensive plants! So I'd say, find out what kind of plants you have, sell them for good money, and replace them when you get to the US, because it isn't worth the hassle of getting them into the US. Anyway, It's an opinion.
MacThayer