European BS - American PhD (Graduate Admission)
I don't think there will be a huge problem in taking a European bachelor's degree to a US institution, so long as you do a little explanatory work in getting ready to apply. The reason for this is that in those first two years, you will often have more major-specific work than most US students will have completed in three years!

So, I would recommend contacting the graduate admissions of programs you're interested in applying to, and explaining your situation to them. Take a look at the undergraduate programs they offer—and in particular, the list of required courses, and show that you have a similar amount of preparation (or more!). Then ask if there's anything else that you need to do.