This is all so much noise. Even proponents of the UBC admit that background checks don't prevent criminals or other restricted persons from getting weapons when they want them. They simply steal them or buy them on the black market. The only people being constrained by the law are law abiding citizens, which to my mind, means that it fails the effectiveness test required to restrain a constitutional right.
Whether or not people consider universal background checks a reasonable measure, imho it craps all over several rights and should either be dropped from consideration or reworked into a proposed constitutional amendment.