Pius bullied the bishops directly. When one Archbishop Bathiarian of Armenia refused to support Pius' push for infallibility, Pius actually went so far as to try and get the papal police to arrest his personal secretary, sparking a small riot in the process. The other Armenian bishops were so frightened that they immediately asked permission to return home. They were denied, but two were smart enough to flee anyway.
Pius used financial pressure on the bishops. Well over 350 bishops attending the council were financially dependent upon the Vatican, without which they would be in dire straights. Pius did not hesitate to take clear advantage of this fact, threatening any who dare dissent with total cut-off from Vatican coffers. Enforcement was achieved by requiring all voting to be done in public - and this tactic worked more than probably any other.
With all of this going on, is it any wonder that many simply stopped attending meetings? Bishop Felix Dupanloupe wrote in his diary: "I'm not going to the Council anymore. The violence, the shamelessness, even more the falsity, vanity, and continual lying force me to keep my distance." Bishop Lecourtier from France, who was so discouraged that he threw his notes into the Tiber river and simply went home only to have his bishopric taken away for his trouble, complained:
- An imposing minority, representing the faith of more than one hundred million Catholics, that is almost half the entire Church, is crushed beneath the yoke of a restrictive agenda, which is contradicts conciliar traditions. It is crushed by commissions which have not been truly elected and which dare to insert undebated paragraphs in the text after debate has closed. It is crushed by the absolute absence of discussion, response, objections, and the opportunity to demand explanations; by newspapers which have been encouraged to hunt the bishops down and to incite the clergy against them.
One estimate had Pius's support at only about 50 bishops at the opening of the First Vatican Council with about 130 opposed and the rest undecided (Of 1050 bishops and others eligible, 800 attended the council, half of them representing European dioceses, and a majority of the rest, European missions abroad. The Americas had 100 representatives).
But after Pius got done with them, 533 of the 598 left in Rome voted his preference. The two who voted against followed Galileo's example by dropping to one knee in front of the Pope after the final tally was announced and declaring "Now I believe." In the following month, the 63 who abstained all eventually consented to the decree and the Pope became infallible through what was ultimately a unanimous vote.
Sources:
How the Pope Became Infallible, by August Berhard Hasler.
Infallible? - An Unresolved Enquiry, by Hans Küng.
Pope-Pourri, by John Dollison.
A Concise History of Christianity, by R. Dean Peterson.

