Is the Catholic priesthood biblical?

Yes, the ordained priesthood is in the New Testament under the word presbuteros, which is where the English word priest actually comes from, and the ordaining of those men by a higher authority through the laying on of hands is described plainly in Acts and in the pastoral epistles. Let me deal with the vocabulary first, because most of the objection lives there. Protestants like to say the New Testament has elders, not priests, and that Rome invented a sacrificing caste later. The word in Greek is presbuteros. It appears over sixty times in the New Testament. It passed into Latin as presbyteri, and from presbyteri through Old English preost we get the English word priest. That is not a Catholic trick, it is in Webster's. The Douay-Rheims translates presbuterous as priests for exactly that reason. So when James 5:14 says let him call in the presbuteroi of the church, the translation "priests" is not a gloss laid over the text. It is the word. There is a second Greek root that tells you something about the office itself. Hieros, which gives us hiereus for priest in Hebrews 5:6 and Revelation 1:6, and hierateuma for priesthood in 1 Peter 2:5 and 2:9, and from which we get the English word hierarchy. The Latin is sacerdos. Both languages associate the priesthood with holiness and with power, with something set apart because it is dangerous to handle carelessly. The Hebrew root qadosh means to be set apart, to be hallowed. The whole Levitical code was designed to protect people from the inherent power of sacrifice. That is the family of ideas the New Testament is drawing on, and it is not a family of ideas about volunteer congregational administrators. Now the structure. In Titus 1:5 Paul writes, for this cause I left you in Crete, that you should ordain priests in every city, as I also appointed you. Look at the chain of authority in that one sentence. Paul could not command Titus to ordain unless Paul stood above Titus, and Titus could not ordain unless he stood above the men he was ordaining. That is three tiers, and it is in the text. Same in Acts 14:23, where elders are ordained in every church, and in 1 Timothy 4:14 and 2 Timothy 1:6, where Timothy's gift comes through the laying on of hands. The patristic evidence consistently distinguishes the episkopos from the presbuteros. Chrysostom, commenting on 1 Timothy, says flatly, he speaks not here of presbyters but of bishops, for presbyters cannot be supposed to have ordained a bishop. By the second century the terminology had settled: the episkope became a bishop over a diocese and the presbuteros a priest over a single church. The rite itself is old and specific. The Council of Chalcedon, under Pope Leo I, prescribes it: when a bishop is ordained, two bishops hold the book of the Gospels over his head while one pronounces the blessing and all the other bishops present touch his head with their hands. When a priest is ordained, the bishop holds his hands over the man's head and all the priests present hold their hands close to the bishop's. When a deacon is ordained, the bishop alone lays hands, because the deacon is consecrated for the ministry and not for the priesthood. Somebody in the fifth century was being extremely careful about who laid hands on whom, which tells you they did not think it was a formality. The usual counter-text is 1 Peter 2:5 and 2:9, the royal priesthood. All Christians are priests, we are told, so an ordained priesthood is redundant. But read the whole passage. Everything in it is spiritual. Christians are not literal stones, they are not a literal house, they are not a literal nation, and they are not offering literal bulls and goats. Peter is contrasting the New Testament people with the Old Testament people by means of figures. He is talking about the Church at large in the spiritual sense, not about her leaders. And Peter cannot be abolishing an ordained ministry in chapter 2 when the same New Testament spends 1 Timothy 3 listing sixteen qualifications for the office of bishop, including that he not be a recent convert. You do not draft eligibility rules for an office that everybody automatically holds. Hebrews supplies another argument. If Christ is a priest forever after the order of Melchizedek, who offered bread and wine, and if his priesthood is permanent rather than passing, then the New Covenant has a priesthood, and Hebrews 13:10 says we have an altar. An altar implies a sacrifice, and a sacrifice implies someone appointed to offer it. Trent says it in so many words in Session 22: at the Last Supper Christ established the apostles as priests of the New Covenant and ordered them and their successors in the priesthood to do what he had done. And the same Session says the victim is one and the same, the one who now offers through the ministry of priests is the same one who then offered himself on the cross. The priest at the altar is not a substitute for Christ. He is the instrument through whom Christ offers. One last point about who the man is. The grace of the sacraments works ex opere operato, from the work performed. Its power does not come from the holiness of the minister. A priest in serious sin still confects a valid Eucharist and gives a valid absolution. That is a mercy God built into the system, precisely because he knew what kind of men would be handling it.