Does the public think that the U.S. government is the only appropriate organization to solve the waste problem?
No, quite the contrary. A recently published three-year study from Stanford University recommends that the United States reset its nuclear waste program by moving responsibility for commercially-generated, used nuclear fuel away from the federal government and into the hands of an independent, nonprofit, utility-owned and -funded nuclear waste management organization.
Additionally, a (2018) survey done by the highly respected firm GfK Global, was designed to reach a representative cross-section of the American public. Their poll found that 70% of Americans think the private sector should be able to propose solutions, and over 90% believe that allowing innovation in nuclear waste disposal would be a good thing to do. View the results of the GfK survey.