Wills basically says that the problem is that decades after a priestless Church of liberal Protestants began, somebody decided to cook up a priesthood so as to exert control over the Church. They cooked up the Eucharist to give the priesthood some excuse for existence and then wrote the letter to the Hebrews to invent a priesthood. Christians read this anonymous book and with the brainless docility of complete fools then accepted this newfangled priesthood because of this anonymous book.
It's the sort of stuff that a moderately clever progressive dissenter can get away with in a culture like America where even the Catholics are largely Protestants who get what information they have about the faith from Protestant and post-Protestant radio and TV. And in our present culture where the episcopacy has not covered itself in glory and people are inclined to greet all claims of faith with skepticism, it is greeted with--paradoxically--utter and complete credulity. In third millennium America, Will$ $ell$.
But only a post-Protestant who imagines that the origins of Christianity lie in somebody writing The Book and then others coming along and building a Church on The Book could possibly suppose that the Church began as a priestless, non-sacrificial religion that only decades later suddenly transmogrified into a priestly sacrificial one because some anonymous dude wrote the letter to the Hebrews and managed to get suckers who were 2000 years stupider than Garry Wills to accept it as Scripture and then construct a priestly system and impose it on the Church.
In fact, of course, Hebrews imposes nothing. Rather, it reflects what the Church has already been doing: offering the sacrifice of the Eucharist since day one. That's why the book is (eventually and only with lots of debate) canonized: because it reflects the faith and practice of the Church, not because it was imposed by main force somewhere around 90 BC by a revisionist Church that cooked up a priesthood 60 years after the Church's founding.
It is Jesus who identifies the Eucharist with the Passover, John who identifies him with the Passover Lamb, and the whole shooting works with the Passover sacrifice. In 1 Corinthians 10, Paul contrasts the Eucharist with the sacrifice of Gentiles to pagan gods (translation: it's a sacrifice). And where there is sacrifice, there is a priesthood. What Hebrews exists to do is explain how this sacrificial priesthood contrasts with the Levitical sacrificial priesthood and how it is "We have an altar from which those who serve the tent have no right to eat". (Hebrews 13)
Finally, regarding the question of Melchizedek: Wills argues (like he knows) that Melchizedek is a Canaanite warlord priest--in short, a pagan. In fact, all we know about him comes from four verses in Genesis. Because he appears from nowhere and vanishes without a trace, the author of Hebrews, in typical rabbinic fashion, describes him thus, "He is without father or mother or genealogy, and has neither beginning of days nor end of life, but resembling the Son of God he continues a priest for ever." He is a "numinous" figure. Somebody who just shows up in the narrative as an immensely august presence. How august? Again, in a sort of playful rabbinic fashion, the author of Hebrews says he was so august that even the guys who receive the tithes from Israel, the Levites, paid him tithes in the person of their ancestor Levi, who was Abraham's heir:
See how great he is! Abraham the patriarch gave him a tithe of the spoils. 5 And those descendants of Levi who receive the priestly office have a commandment in the law to take tithes from the people, that is, from their brethren, though these also are descended from Abraham. 6 But this man who has not their genealogy received tithes from Abraham and blessed him who had the promises. 7 It is beyond dispute that the inferior is blessed by the superior. 8 Here tithes are received by mortal men; there, by one of whom it is testified that he lives. 9 One might even say that Levi himself, who receives tithes, paid tithes through Abraham, 10 for he was still in the loins of his ancestor when Melchizedek met him. (Hebrews 7:4-10)
The only other time we meet Melchizedek is in the psalm of a king who appears to have been a bit obsessed with him: David. That's not surprising since David has made both his political capitol and his cultic center in the city Genesis calls "Salem": Jerusalem. It was there that Melchizedek was king. Significantly, the "name" Melchizedek is not a name at all but a title, just as "Christ" is not Jesus' last name, but a title. It means "King of Righteousness" and he behaves like priest king. He not only rules Salem as king but offers sacrifice which Abraham honors and receives tithes Abraham offers.
Think about this: the entire reason Abraham is in the Holy Land is because he is separating himself from the worship of pagan gods and pursuing the worship of the one true God. The way you worship God is to offer sacrifice. Now this Melchizedek character shows up, acting as a priest and Abraham completely honors his priesthood and his sacrifice--something he does with no pagan. In short, he regards Melchizedek as a priest of the true God, not as a priest of Baal or some other pagan cultic deity. Why? We don't know. Both Jewish and Christian pious tradition identified Melchizedek with Shem, the son of Noah, but we needn't accept that. Whatever the reason, Abraham sees Melchizedek not as a pagan Canaanite priest, but as a priest of the same God he worships. For David, this matters because David identifies himself with Melchizedek and behaves like a priest king too, even though he is of the tribe of Judah, not Levi. So when he enters Jerusalem with the ark of the covenant, he dances before the ark in a linen ephod--that is, a priestly garment. If you want to get the hang of it, imagine Obama donning a stole and blessing the crowd after his inauguration: that's how weird it is for the king to be taking on this quasi-priestly role. And as he prepares to hand the kingdom over to his son Solomon, he writes a coronation ode in which, for the second and last time in the entire Old Testament, we hear the name of Melchizedek as David tells his son, "You are a priest forever after the order of Melchizedek." So the Son of David possesses a priesthood prior to and superior to the Levitical priesthood.
One final point: it should be noted that in antiquity you don't just offer sacrifice any old place. There are cultic sites where some event or something of remote antquity or even geographic elevation (the higher, the closer to God) sets the place apart. So after God appears to Jacob in a dream, he designates that place "Bethel" or House of God and it becomes a cultic site. Conversely there are places that are accursed or haunted (such as the Valley of Hinnom, where children were sacrificed to Moloch: it becomes the source of the word "Gehenna" or "hell"). You don't use such places for cultic observances.
We see this reflected in Exodus 15. In Exodus 15, Israel celebrates with the famous Song of Moses, an antiphonal hymn praising God for the deliverance at the Red Sea. In the course of this hymn we read a puzzling passage:
Thou wilt bring them in, and plant them on thy own mountain, the place, O Lord, which thou hast made for thy abode, the sanctuary, Lord, which thy hands have established. (Exodus 15:17)
The reason this passage puzzles many people (and leads many modern scholars to think it must have been composed centuries after the Exodus) is this mention of "thy abode" which refers to the Temple, which would not be built until the reign of Solomon shortly after 1000 BC, centuries after the death of Moses. The conclusion that scholars too easily reach is that Moses could not have had any notion of building a sanctuary in Jerusalem. But this overlooks the fact that Moses obviously has a very clear awareness of the tradition of Abraham, Isaac and Jacob, a tradition that is the entire basis, after all, for the events of the Exodus. The whole reason for the Exodus and the gift of Canaan to the people of Israel is, as God repeatedly tells Moses, because he has remembered his covenant with Abraham, Isaac, and Jacob. Thus, so far from having no notion of a sanctuary to be built in a particular place in the land of Canaan, we are told instead:
But when you go over the Jordan, and live in the land which the Lord your God gives you to inherit, and when he gives you rest from all your enemies round about, so that you live in safety, then to the place which the Lord your God will choose, to make his name dwell there, thither you shall bring all that I command you: your burnt offerings and your sacrifices, your tithes and the offering that you present, and all your votive offerings which you vow to the Lord. (Deuteronomy 12:10-11)
When do we see Israel enter its "rest" then? 2 Samuel 7:1-2 tells us:
Now when the king dwelt in his house, and the Lord had given him rest from all his enemies round about, the king [David] said to Nathan the prophet, “See now, I dwell in a house of cedar, but the ark of God dwells in a tent.”
Note that the "rest" which God promised Israel in Deuteronomy is bound up with the conquest of the land and with the establishment of the Temple. It is when Israel, under David, entered its rest that David now begins to implement the command given in Deuteronomy 12:10-11 to establish a "place" (not a movable Tabernacle) of sacrifice and offering where God will make his name to dwell. It is also interesting to note that Deuteronomy does not tell us where this "place" is.
But David knew: it was Jerusalem, which is where he brought the Ark of the Covenant (2 Samuel 6). How did he know? Because he is aware of the same Abrahamic tradition that Moses is also aware of in the Song of Moses. For not only is it the city of Melchizedek, it is the site of the offering of Isaac, which sealed God's covenant with Abraham. This had taken place on Mount Moriah, one of the hills Jerusalem is built on (cf Genesis 22; 2 Chronicles 3:1). So there is excellent reason to think that Moses, who knew the story of Abraham and Melchizedek very well, had good reasons for aiming to place the "abode" of God in Jerusalem long before it would be physically possible for Israel to do so.
So, in fact, there is plenty of reason for the New Testament to see Jesus as a priest, the Eucharist as a sacrifice, and the ongoing celebration of the Eucharist (the command, after all, is "Do this in memory of me" meaning that it is to happen in perpetuity), requiring a new covenant priesthood deriving from the son of David's Melchizedek priesthood, just as Jesus himself points out when he claims to be the Son of David and applies Psalm 110 to himself.