As of right now, there are no laws in place dictating that Nazis may not express their beliefs. Their 1st Amendment rights ensure that they are perfectly free to do so. However, this does not mean that they will face no consequences for their hateful rhetoric. Put simply, freedom of speech does not mean freedom from consequence. This effect can be seen in other areas of society. For example, a person has the freedom to confess to a robbery or threaten to assassinate the president, but they are not free from the legal and social repercussions of their words.
Additionally, this argument provides no justification for the importance of upholding the U.S. Constitution; it simply treats it as a good in and of itself, rather than explaining why it is just or beneficial.