The best source for this discussion is probably still Georges Dumézil, Archaic Roman Religion (orig. Editions Payot, Paris: 1966; translated by Krapp, Johns Hopkins 1996). He goes through the interesting history of this idea, called predeism or dynamism. It was most powerfully argued by H. J. Rose, who sought to ferret out the most elemental element of Roman belief, the "mana." He arrived at the Roman concept of numen (so his Primitive Culture in Italy 1926 and later Roman Dynamism 1947). He separated out a few major deities (Jupiter, e.g.) and called the rest "polydaemonism" (to borrow daemon from the Greek): "an accumulation of beings, each capable of accomplishing a single action but without any existence, beyond their specialty, either in the cult or in the imagination" (Dumézil p.20ff).

From there, Dumézil goes on to attack Rose' conception and to argue that the Latin word numen is being misunderstood. He marshals ancient evidence of its (admittedly complicated) use and the ancients' apparent understanding of the concept. He then goes on to talk about the Latin word for an actual, bodied god, deus, and marshals some Indo-European evidence (only in its adolescence as a discipline in 1966).

That is Dumézil's chapter 3. In Chapter 4, he begins by acknowledging that archaic Roman religion did in fact have a plethora of "minor" powers, but he cautions us that they must be "interpreted correctly." It was, in fact, impossible to move about in the Roman physical space without bumping into, stepping on, or passing through a minor numen. Powers inhabited the fountains, the cobblestones, the wheels of carts, the hinges of doors, everything.

Dumézil's book is now a bit dated, but as I said, he is still a great place to start, especially for the history of scholarship on Roman religion leading up to his time and his pugnacious anti-primitavist arguments.