Here is how "euhemerism" is defined by some mythicists.
First, Dr Robert M Price, in
Deconstructing Jesus, page 250 (my bolding):
[Paul Veyne] describes how thinkers of Greek and Roman antiquity, including Diodorus, Cicero, Livy, Pausanias, and Strabo, approached mythic figures such as Theseus, Herakles, Odysseus, Minos, Dinoysus, Castor, and Pollux: They readily dismissed the supernatural tales of their heroes' divine paternity and miraculous feats but doggedly assumed there must have been a historical core that had been subsequently mythologized. Their task as historians was to distill the history from the myth and to place the great figures where they must have occurred on the historical time-chart... The whole approach earned the name of Euhemerism, from Euhemerus who originated it. The idea was to assume that all ancient gods were glorified ancestors or historical culture heroes. Though no mundane, "secular" information about them survived, it had to be assumed that a genuine historical figure lay at the roots of the myths.
See how Price notes that the ancient writers "readily dismissed
the supernatural tales of their heroes' divine paternity and
miraculous feats". That certainly doesn't describe the Gospels as the end product of euhemerizing. And Price correctly defines Euhemerisim as gods who were "glorified ancestors". Not "glorified god-men", which is a bit of an oxymoron.
And here is David Fitzgerald, mythicist (my bolding):
http://www.nazarethmyth.info/Fitzgerald2010HM.pdf
Most people have never heard of the Greek mythographer Euhemerus; and so many might be surprised to find that they are Euhemerists on the subject of Jesus. That is to say, though they may not believe Jesus was the divine Christ that Christianity venerates as the Son of God and savior of the world, and may regard accounts of the miracles and wonders attending him as mere legendary accretion; nevertheless they certainly believe there had to have been a central figure that began Christianity. Perhaps he was just a wandering teacher, or an exorcist, an apocalyptic prophet or a zealot who opposed the Romans.
Again, Fitzgerald notes that the end product of Euhemerism is just a man, perhaps a wandering teacher. But if you take Carrier's definition, the
Gospels are the end product.
Even the late Acharya S gets the definition right!:
http://freethoughtnation.com/rabbi-did-jesus-actually-exist/
... as concerns [Rabbi] Singer’s description of mythicists, in reality there are not two camps of mythicists, one which opines Christ is a myth through and through, and one that believes there’s “some guy” at the core of the story, to whose mundane biography were added fabulous fairytales. This latter camp is, in fact, called “euhemerist” or “evemerist,” not mythicist...
Despite his protestations against other “very biased” scholars’ conclusion without any real evidence that Jesus existed, [Rabbi] Singer claims again that no one can know what really happened but it is likely that such a person did exist. Hence, the rabbi is an evemerist, but he believes in this way only because there were plenty of apocalyptic preachers in the Levant during Jesus’s alleged era.
Second Century apologists also invoked the name of Euhemerus to show that the pagan gods were only men -- see my examples below. It wouldn't make much sense to have them claim "Your celestial gods are really men who ascended to heaven as gods". No, their claims were that Euhemerus showed that the pagan gods weren't gods at all, merely men. That is why Euhemerus was accused of atheism.
Here are references to Euhemerus by Second Century Christian apologists:
Theophilus of Antioch:
http://www.earlychristianwritings.com/text/theophilus-book3.html
And to speak of the opinions of the most atheistical, Euhemerus, is superfluous, For having made many daring assertions concerning the gods, he at last would absolutely deny their existence...
The idea that Euhemerism can encompass the result of proposing "deified man-gods" along the lines of a Gospel Jesus is simply not found.
Here is Minicius Felix:
http://www.earlychristianwritings.com/text/octavius.html
In like manner with respect to the gods too, our ancestors believed carelessly, credulously, with untrained simplicity; While worshipping their kings religiously, desiring to look upon them when dead in outward forms, anxious to preserve their memories in statues, those things became sacred which had been taken up merely as consolations...
Read the writings of the Stoics, or the writings of wise men, you will acknowledge these facts with me. On account of the merits of their virtue or of some gift, Euhemerus asserts that they were esteemed gods; and he enumerates their birthdays, their countries, their places of sepulture...
Finally, here is pagan philosopher Plutarch on Euhemerus:
http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/B.html
[We should not be] opening wide the great doors to the godless throng, degrading things divine to the human level, and giving a splendid licence to the deceitful utterances of Euhemerus of Messenê, who of himself drew up copies of an incredible and non-existent mythology, and spread atheism over the whole inhabited earth by obliterating the gods of our belief and converting them all alike into names of generals, admirals, and kings, who, forsooth, lived in very ancient times...
Claiming that the gods did not exist, being an atheist with respect to the Greek gods, THAT is what Euhemerus and the euhemerists are famous for. It is not taking a celestial deity and placing it in history
as a god-man. Carrier is simply wrong in how he defines Euhemerism. It isn't fatal to his theory, but it should make you wonder if he is as sloppy towards other topics in his theory.