Your question is more of a "what-if" than something we can answer by looking at the historical record.

If we look squarely at the last line of your question ("In truth, could the U.S. have defeated the NVA if left unrestricted by President Nixon or the feelings of those at home?") then the answer can only be a yes. If the American military had been able to harness the complete might of the national economy and all fighting age males, regardless of other consequences, while doing things like using nuclear weapons then there cannot really be any doubt that America would have won. (Unless, of course, we get into a whole scenario where this escalation / the use of nuclear weapons causes China and the USSR to then deploy their own nukes and then we have MAD and no one wins).

I think what you may really mean to ask is if America could have won if the military had been turned loose just a little more than they were - without going so far as I have imagined above. I think that may require an answer from someone more versed in the history of the war in Vietnam than myself.