Building a machine that can travel at speeds exceeding Mach 3 for a brief period of time is probably well within aeronautical engineering's current capabilities, with today's engines, yes. The innovation with the SR-71 was that it could fly at those speeds for an hour and a half, thanks in part to that JP-7 fuel with its high flash point.

Either way it's unclear why NASA, with its decreasing budget, might feel like they need to be taking this on as a research project.