Newman was not opposed to Papal Infallibility per se as the First Vatican Council met. He was more opposed to what some in the Ultramontanist Party at the Council meant by Papal Infallibility, going beyond faith and morals and into political and social definitions and even verging on Papal Indefectibility, holding that the Pope could make no personal error. Newman was also concerned that some wanted to vest Infallibility in the person, not the office.
As the Council continued and reports demonstrated that his concerns about how the Ultramontane group (and even Pope Pius IX) was treating those who thought the timing for the definition unfortunate, he became more concerned. But he also knew that this was how Councils were: Church History showed him that men and not angels were proposing and debating crucial issues in the Church. Even the early Councils of the Church, defining what the Church believed about the Person of Jesus and His Natures, led to division and confusion. When the bishops left Nicaea, Constantinople, Ephesus, or Chalcedon, new heresies arose and they had to meet again and again to define the truth--and even after the Church's teaching about Jesus was finally expressed, there was schism.
As I told the participants at the Eighth Day Institute's Florovsky-Newman Week:
When Pastor Aeternus was finally voted on, he was pleased to see that Papal Infallibility was narrowly defined; he waited to see how the dissenting bishops responded: securus judicat orbis terrarum! Newman made no public statement except to again deny rumours that he was going to leave the Catholic Church (he had to make these periodically!)
Only when William E. Gladstone, former Prime Minister, published The Vatican Decrees in Their Bearing on Civil Allegiance in 1874 did Newman respond in 1875 with his Letter to the Duke of Norfolk, addressing his counter-argument to the pre-eminent Catholic peer, Henry FitzAlan Howard, scion of a family with two martyrs (Philip Howard and William Howard) in its pedigree. Selecting the 15th Duke of Norfolk as his public correspondent was testing Gladstone’s main contention: that Catholics could not be loyal Englishmen if they accepted Papal Infallibility. Was the Earl Marshall of England, who happened to be a Catholic and a graduate of Newman’s Oratory School, not a loyal Englishman? Did Gladstone really mean that?
We discussed Newman's response to Gladstone's notion that Catholics in England would have to suppress or ignore their consciences in order to accept the doctrine of Papal Infallibility in March when we talked about Newman and Conscience. What Newman also accomplished in A Letter to the Duke of Norfolk was explaining how limited the use of Papal Infallibility was. Again, from my paper:
Besides, he reminded Gladstone, the Pope’s Infallibility is limited to speaking on matters of faith and morals as abstract doctrine and principles, not on individual decisions of what to do or not to do in a certain situation. . . .
In a later chapter, on “The Vatican Definition” Newman emphasizes that the Pope speaks infallibly only under certain conditions:
He speaks ex cathedrâ, or infallibly, when he speaks, first, as the Universal Teacher; secondly, in the name and with the authority of the Apostles; thirdly, on a point of faith or morals; fourthly, with the purpose of binding every member of the Church to accept and believe his decision.When the Pope is speaking his mind on any subject like the interpretation of scripture, economics, history, etc., he is not infallible because “he is not in the chair of the universal doctor.” Even if the Pope makes dogmatic statements in an encyclical, as Pope John Paul II did in The Gospel of Life, reiterating Catholic teaching against abortion, for example, those are not exercises of Papal Infallibility.
Since the definition of Papal Infallibility in 1870, only one Pope has used this power: Pope Pius XII when defining the doctrine of the Assumption of the Blessed Virgin Mary in 1950. In spite of his reservations about the First Vatican Council's conduct, Newman accepted the work of the Council, but he knew that the Church--the whole Church, including the laity and the theologians, needed time to understand the theology and practice of the doctrine of Papal Infallibility. The First Vatican Council was abbreviated by the Franco-Prussian War and the cause of Italian unity, as the Italian Army was soon at the gates; the Papal States were lost and the long period the Pope as "the prisoner of the Vatican" began.
Newman was always ready to obey the Pope and pray for the Pope as this 1866 Sermon preached at the Birmingham Oratory shows. He also helped Catholics and non-Catholics understand Papal Infallibility, providing an explanation that Father John O'Malley, in his book Vatican I: The Council and the Making of the Ultramontane Church, says “soon achieved almost canonical status” by answering Gladstone's objections.