The public overwhelmingly supports NIH-funded research. https://www.aacr.org/about-the-aacr/newsroom/news-releases/n...

The issue, I think, is a large number of people don't realize the NIH or NIS exists or know what they do.

I think most people support them once the realize exactly what they are doing. How could you not when "They research treatments for diseases" is basically all they do.