I'd like to add that the word "serpent" is an inappropriate translation at this point. The Hebrew word is "Nachash." A serpent is a "creeping thing," But the text says that this creature, the Nachash is a beast of the field (or you can read it this way here). At minimum 3:1 compares him to beasts of the field. These are a distinct category from wild animals and from creeping things.
At Genesis 3:1, Nachash is not on the ground creeping on its belly. Perhaps we can imagine it walking with legs. There are certainly egyptian images of snakes with wings and legs.
Genesis 3:14 re-iterates that Nachash was among the animals and wild creatures when he is cursed. Then he is put on the ground to crawl. At this point, the we might translate the term "nachash" as serpent, but nachash doesn't show up again after this until Jacob labels the tribe of Dan as a guardian of israel, or "a serpent (nachash) on the way."
Moses' staff would transform into a nachash Exodus 4:3 and Exodus 7:15. It's interesting to note that Aaron's staff turned into a tannin serpent which was the sea monster created in Genesis 1.
Nachash would show up again in Numbers 21 when God sent fiery serpents (nachash seraphim) as his agent to punish the hebrew people for their rebellion against Moses and God. God then has Moses build another nachash as an icon to which the people must look to be healed. John compares Jesus on the cross to this icon in John 3:14-15, and it is on the Sistine Chapel ceiling.
Amazingly, also, in 2 Kings 18:4, Hezekiah smashes Moses's bronze serpent (nachash) becomes people where WORSHIPING IT. So before Hezekiah's time (possibly back to David and Solomon and perhaps all the way back to Moses, this artifact of the serpent (nachash) icon had survived, in the temple, and was worshipped.
Does this mean that the Genesis 3 text (which everyone agrees was written before Hezekiah - whether the J documentary hypothesis or simply that it was written by Moses).. Does this mean that they saw the Nachash as a deity and protector who was a symbol of life?
We inherit a disgust towards snakes for the post part due to Revelation 12:9 (which I believe points to the tannin of Genesis 1 which is equivalent to the Egyptian Apophis, serpent God of the underworld who was Ra's enemy), but they were seen as symbols of eternal life, due to the shedding of their skin. This was true in Gilgamesh and in the Greek story of Hercules in the Garden of the Hesperides where the serpent was wrapped around the tree of the apples of immortality.
The Emperor Augustus of Rome (Reigned 27BC - 14AD, just around the time of Christ), was thought to have been conceived by Apollo in serpent form according to Suetonius. The Ancient Egyptian Pharaohs wore the raised cobra "uraeus" on their head-dress. In Matthew 10, Jesus tells his disciples to be wise as serpents using the same greek word used in the septuagint in Genesis 3:1.
So back to your original question, it is unclear what the Hebrews thought when hearing that story, but it certainly wasn't that the nachash was a dimminutive evil beast. Hearing about a serpent in a garden would have had people, around the campfire, turning to one another and saying "oh, I love having serpents in my garden, they eat the rodents and not my vegetables! They till up the soil!"
The serpent has special privileged knowledge about God that the woman doesn't seem to have. He knows the consequences of eating of the fruit of the tree of the knowledge of good and bad. What he says happens. He also knows properties of God (that God knows good and bad, affirmed in 3:22).
Or perhaps when the people in the time between Solomon and Hezekiah read the story, they thought of nachash as a deity worshipped in the temple... Or at best as an icon through which obedience to God was obtained according to the story in Numbers.
Perhaps they read the story of Genesis 2/3 and thought that it wasn't the serpent who lied, but the woman who lied about the serpents trickery.
I believe the main reason that we inherit a hatred for snakes is because in the second century, Justin Martyr and others had to create defenses of Christianity to pull members from the cult of Asclepius who was the principle deity... A benevolent god of healing... Who was born of a union between a woman and Apollo (just like Augustus), and was struck down dead by a lightning bold from Zeus because he was resurrecting people (exactly what happens in John as the Jews seek to kill Jesus after he resurrects Lazarus), and then Zeus resurrected him and raised him up to his right hand on Olympus.
We had to fight a marketing battle with Asclepius, so we demonized healings by the serpent icon... Which was Asclepius's symbol. You could go into any Asclepions and find rooms full of non-venemous serpents who could heal you. We still see this marketing conflict play out TODAY on the back of catholic hospital ambulance. The blue star of life contains the rod of asclepius with the serpent, and the name of the hospital probably contains the iconography of the cross. And both of these symbols intersect in Numbers in the nachash raised up to heal the people. Michaelangelo actually painted the rod of asclepius on the Sistine Chapel ceiling in the Numbers 21 painting.
Hezekiah had to destroy the Asherah Poles as well Moses' serpent from inside the Temple. This indicates that there was a ton of polytheistic worship going around. Deuteronomy (and the Shema prayer in Chapter 6 - "God is one") probably comes during the time of this temple restriction period of Hezekiah where there was a move to a more monotheistic theology compared to a polytheistic or henotheistic cult in the temple.
There is plenty of evidence in the bible and in archaeology that the serpent may have been seen as a deity, but as the post-exilic assemblers of the Torah saw it, they were certainly staunch monotheists and would have none of that. For them, the serpent was a created animal of the field just like all the others.
I recommend a text by Princeton Seminary Professor, Archaeologist, and united methodist ordained minister, James H. Charlesworth.
Charlesworth, James H. The good and evil serpent: How a universal symbol became christianized. Yale University Press, 2010.
It has a ton of amazing stuff on this topic and is a really accessible read. The guy does a careful exegesis of John 3:14-15 and that takes him through Genesis 3, Numbers, and Kings as well. He has a ton of archaeology including an early roman menorah made of snakes for the candle holders, and a bunch of other amazing stuff that will blow your mind when thinking about Genesis 3 next time you read it.