I would suppose that traditionally, evidence had this broad meaning that I seek, and that is why "empirical evidence" is a popular phrase.
What I would like is a word that refers to a broad notion that encompasses theoretical arguments, as well.
I want to refer to everything substantive that an individual has brought to a discussion: not only the empirical evidence (such as demonstrations or references), but also the non-trivial theoretical points that they have made.
For instance, if I was arguing about taxes with someone, and they say "Raising taxes is a bad idea, because the government already has too much power", then unless I completely reject the premise that the government has too much power, this should be considered "theoretical evidence" for their position that "Raising taxes is a bad idea".
I can't think of a better word than evidence, but I don't think people will understand what I'm talking about if I use it this way, without explaining what I mean first.