With rare exception, the secular press denounced the definition as "a scheme of spiritual, social and coercive despotism," which made the pope "temporal ruler of the world, and authorizes him to supplant, by force, every form of civil government."  By this act, "Romanism declares war against intelligence; as three hundred years ago it commanded the earth to stand still in its course among the stars, with the same authority and the same impotence it today commands the human race to stand still in its greater career of advancement and hope.
It is a sad end for one of the mightiest institutions of history; but henceforth the Papacy goes its own way of decay aside from the great movements of the world."  While these sentiments are now modified, at least in their tone of ridicule and fear of papal aggression, the substratum of repugnance towards the Church's infallibility has not radically changed.
But it is also nuanced, and to understand it we need to make some distinctions that are too often cathedra, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole Church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his Church to enjoy in defining doctrine concerning faith or morals.
What the Council is describing here is the pope’s exercise of what is called his “extraordinary Magisterium,” as opposed to his “ordinary Magisterium” or everyday teaching activity in the form of homilies, encyclicals, etc.
Normally external divine assistance is enough, i.e., by so arranging circumstances as to preclude the possibility of a mistake; although, if need be, an actual supernatural influx in the mental and volitional faculties will not be wanting.