It's already well nigh impossible to study newly discovered "native" human remains. If you're working on an site and uncover human remains, all work stops, you call in the state archaeologist (or whoever the authority is - a few states don't have a state archaeologist), who notifies local tribes, and in the end, they pretty much end up being reburried right then and there. If you're lucky, you can continue to dig in another part of the site... more often, the whole area is closed. So, what happens more often is archaeologists who uncover human remains simply cover them back up, close the pit (or don't put one there if it's still at the survey stage), move over a few meters and don't say a word. If you hit a second set of remains, THEN you call in the state archaeologist (because you might have a burial ground).
The even bigger problem this legislation will cause is in the area of artifacts. NAGPRA doesn't just apply to human remains; it also applies to grave goods and any artifacts deemed "sacred" by native tribes... that includes items that were not collected archaologially, but were gathered during ethnological studies in the 19th and early 20th centuries.
Many museums and archaeologists have worked with Native groups to make reasonable sense of the law as it stands so that both parties can be satisfied, but there are some extremists on both sides. Researchers who feel they shouldn't have to give ANYTHING back and should have free reign in the name of science and also Indians who feel that EVERYTHING should be returned and no one not of Native descent has the right to touch/interpret/study anything Native. This change would fuel the fires between those two groups (giving the extremist native groups more claim to many things) and infuriate the extremist researchers, upestting the relatively decent balance that has been worked out by the majority of both researchers and Native Americans... on the artifact issue that is.