New World Language Families

[Polycarp]

There has been extensive work over the years by anthropologists and comparative philologists attempting to classify and relate the various languages of aboriginal North and South Americans. But every time I attempt to read up on this, I seem to get results that are far more indebted to individual scholars' opinions than reporting a consensus of scholarly opinion. E.g., is there such a family as "Andean-Equatorial" that includes Quechuan, Aymaran, Guarani, Tupi, and Arawakan? Are Iroquoian and Siouxan truly related, and are they part of a larger group? Is the concept that all non-Athabascan aboriginal Indian languages are interrelated the blue-sky hypothetical concept that it appears to be, or is there actually some consensus on the view?

So what I'm asking here is if anyone can produce, or link me to, a coherent description of generally accepted major New World language families, with something of their characteristics and principal constituent members. I'm aware of Ethnologue, of course, but I don't seem to be getting the coherent answer I'm looking for in terms of clear statements of generally accepted groupings of significant size, from looking at it. Does anyone want to take a crack at this?