St. Irenaeus wrote to Pope Victor, suggesting leniency, but presupposed that he had the authority to make a sweeping decision one way or the other.
If you read Eusebius' account of Irenaeus' letter to Victor and the responses of others (Church History, 5:23-25), you see that there's no implication that Irenaeus presupposed papal authority on Victor's part, and you see that the bishops who initially disagreed with Victor on the matter in dispute continued to disagree with him. Polycrates, bishop of Ephesus at the time, sent Victor a letter of rebuke, applying the principle of Acts 5:29 to Victor's threat of disfellowship.
The most that can be cited in support of a papacy from Eusebius' account is Eusebius' comment that:
"Victor, who presided over the church at Rome, immediately attempted to cut off from the common unity the parishes of all Asia, with the churches that agreed with them, as heterodox; and he wrote letters and declared all the brethren there wholly excommunicate." (5:24)
Even if we assume, for the sake of argument, that Victor thought he was exercising papal authority, does it follow that Irenaeus assumed such authority when he wrote his letter arguing against Victor's course of action? No. I don't know what Dave's line of thinking is one this issue, but he may be assuming that if no denial of papal authority is present in the portions of Irenaeus' letter quoted by Eusebius, then Irenaeus must have agreed with Victor on the subject. But that conclusion doesn't follow from the premise. And there's no reason to conclude that Victor claimed papal authority to begin with.
But before I explain why, we ought to consider the implications of the absence of a papacy in Irenaeus. Three sources of Irenaeus' writings are extant today. We have his Against Heresies, his Demonstration Of The Apostolic Preaching, and some fragments from other documents no longer extant. I've never seen a Catholic, as far as I recall, argue for evidence of a papacy in Irenaeus' Demonstration Of The Apostolic Preaching. And discussions of Against Heresies center around the passage I discussed earlier in this series. That leaves us with the fragments. The fragments of Irenaeus' letter to Victor, accompanied by Eusebius' commentary, are the only alleged evidence for a papacy I've seen cited from the fragments. Notice how weak the case for a papacy in Irenaeus is. We have no reason to conclude that he believed in the papacy or that he believed in any concept that implies the papacy. Rather, he believed in a Roman primacy that he doesn't define as jurisdictional and he gives reasons other than a papacy for it, he apparently didn't believe that Peter had authority over Paul, and he says nothing of a papacy in hundreds of pages of material in which he frequently discusses related issues (authority, church government, the apostle Peter, etc.).
Getting back to Victor, should we conclude that he claimed papal authority? The portion of Eusebius' account that has the most potential for leading to the conclusion that he did assert such authority is Eusebius' comment that Victor "declared all the brethren there wholly excommunicate" (5:24). Might such an action be a result of a belief in papal authority? Yes. The problem for Catholics like Dave, however, is that Victor's actions are also consistent with his not having viewed himself as a Pope.
As an illustration of the variety of potential meanings Eusebius' account could have, consider another incident I mentioned in an earlier response to Dave. The Catholic scholar Klaus Schatz wrote the following about responses to the doctrinal inconsistencies of the Roman bishop Vigilius in the sixth century:
"The emperor in turn called a council at Constantinople (the Second Council of Constantinople, 553) made up only of opponents of the three chapters. It not only condemned those three chapters but even excommunicated the pope. This was a unique case of an ecumenical council setting itself clearly against the pope and yet not suffering the fate of Ephesus II. Instead, over time it was accepted and even recognized as valid by the pope. The council got around the papal opposition by referring to Matthew 18:20 ('Where two or three are gathered in my name. . .'): no individual [including the Pope] could therefore forestall the decision of the universal Church. This kind of argument was invalid, of course, because the pope was not alone; the entire West was behind him, and yet it was not represented at the council. Broken in spirit, Vigilius capitulated after the end of the council and assented to its condemnation of the three chapters. The result was a schism in the West, where the pope was accused of having surrendered Chalcedon. A North African synod of bishops excommunicated the pope, and the ecclesial provinces of Milan and Aquileia broke communion with Rome. (Milan returned to communion only after fifty years; for Aquileia the breach lasted one hundred and fifty years, until 700)." (Papal Primacy [Collegeville, Minnesota: The Liturgical Press, 1996], p. 53)
Presumably, Dave would argue that Second Constantinople was claiming authority over the Pope, but didn't have it, and that the synod in North Africa was breaking fellowship with the Pope without claiming to have an office of jurisdiction over him. If he wants us to believe that papal authority was involved in the case of Victor, he ought to argue for that conclusion rather than just assuming it. And if he wants us to believe that other churches agreed with such an assertion of papal authority on Victor's part, despite the negative reaction to Victor that I've outlined above, Dave would need a further argument to that effect.
Let's go back to the beginning of Eusebius' account:
"Synods and assemblies of bishops were held on this account, and all, with one consent, through mutual correspondence drew up an ecclesiastical decree, that the mystery of the resurrection of the Lord should be celebrated on no other but the Lord’s day, and that we should observe the close of the paschal fast on this day only....But the bishops of Asia, led by Polycrates, decided to hold to the old custom handed down to them." (5:23-24)
There was an attempt to reach agreement through a consensus of regional synods. Most agreed with Victor's position on the issue, but the churches of Asia Minor didn't. Might Victor have asserted papal authority at that point? Yes, but he also might have asserted the authority of an ecclesiastical consensus. The synods and exchange of letters among the churches had demonstrated that the position Victor held was the majority view. If he thought that the widespread agreement on the issue was sufficient to settle the matter, he might have considered the actions of the Asian bishops in maintaining their position inappropriate and deserving of disfellowship. He knew that he had the majority on his side and that synods, an exchange of letters, and other actions had already been taken to establish the majority status of his position. His attempt to "cut off from the common unity the parishes of all Asia" (5:24) may have been based on what Eusebius mentions: the common unity expressed by the synods, not papal authority.
George Salmon wrote:
"Suppose it had been Irenaeus who had rashly broken communion with the Asiatic Churches; suppose that Victor had then written a letter to Irenaeus, sharply rebuking him, and had written also to other bishops, warning them not to separate from those who had been unwarrantably excommunicated; and suppose that in consequence of this action of Victor’s the threatened schism had been averted, would not that have been paraded as a decisive proof of Papal Supremacy?" (The Infallibility Of The Church [London, England: John Murray, 1914], p. 386)
And it's worth noting that Eusebius tells us that Victor attempted to cut off the Asian churches. His effort failed. Even bishops who agreed with Victor's position on the issue under dispute "sharply rebuked" him (5:24). In his letter to Victor, the Ephesian bishop Polycrates mentions that the synod in Asia Minor had been held at Victor's request (5:24), so it seems that Victor had more of an interest in settling the issue than other bishops had. They were satisfied with allowing the disagreement to continue, but Victor wasn't.
Throughout this account, Eusebius speaks of Victor as one church leader among others, never referring to him as a Pope. (The concept of the papacy is, in fact, absent from Eusebius' entire church history.) He refers to Victor as one local church leader holding a synod in his region while other local church leaders held synods in other regions (5:23). He refers to him as "Victor, who presided over the church at Rome" (5:24). The same could be said of a Pope. But why only mention Victor's regional authority if he had universal jurisdiction and was the infallible foundation of the church? Why would Eusebius repeatedly refer only to such regional authority? Eusebius goes on to say that Irenaeus "conferred by letter about this mooted question, not only with Victor, but also with most of the other rulers of the churches" (5:24). Again, Victor is referred to as one ruler of a church among others. He made himself prominent in this dispute over the celebration of Easter, both by initiating the discussion and by trying to cut off the Asian churches from the common fellowship when they disagreed with his position. But he was a regional church leader among other regional church leaders, not a Pope, despite his prominence in this particular dispute.