The House just passed H.R. 8 which would require universal background checks for all sales including private party sales. I doubt it will get by the Senate, but who knows. There are bound to be a few traitors.
https://www.govinfo.gov/content/pkg/BILLS-117hr8ih/pdf/BILLS-117hr8ih.pdf
https://www.govinfo.gov/content/pkg/BILLS-117hr8ih/pdf/BILLS-117hr8ih.pdf