New EU member states will not enjoy visa-free travel to the USA anytime soon unlike the "old" EU member states. Of the 15 current members, only Greek citizens must apply for a visa to travel to the US. On the other side of the continent, only Slovenia meets the criteria for visa-free travel to the USA out of the new member states.
Furthermore, the accession countries will not be able to invoke a law that would require support from other EU member states on the issue.