For the Cristeros to succeed, they needed massive help from US Catholics. They got some, but not as much as they hoped for, as explained in Julia G. Young,
Mexican Exodus: Emigrants, Exiles, and Refugees of the Cristero War https://books.google.com/books?id=q8TNCQAAQBAJ&pg=PT111
(1) The Church hierarchy: "By the mid-December of 1926, it was clear to the leaders of the Liga that no financial support would be forthcoming from the US Catholic hierarchy.20 The reticence of the US Catholic leadership was perplexing and frustrating to Mexican Cristero supporters, but it can be understood within the political context of the period. While US Catholic leaders were indeed opposed to the Calles government, and many of them supported the Cristero cause, they were caught in a sticky diplomatic situation. If they provided Mexico's Cristero militants with direct aid-—especially weapons-—they would be breaking the law, for it was illegal to help a foreign revolutionary movement that aimed to depose an ally of the United States. Given the anti-Catholic sentiment that persisted within American political culture, the US hierarchy felt that it was in too precarious a position in the political firmament of the United States to collectively support the violent overthrow of the Mexican government."
(2) The Knights of Columbus: "The US Catholic bishops were not the only potential source of assistance, however, and Mexican Catholic exiles had great hopes that another Catholic organization, the Knights of Columbus, would prove more helpful. In February of 1926, Liga leader Rene Capistrin Garza and Jose Gaxiola-—along with the Jesuit priest Carlos Maria Heredia, one of the early founders of the Catholic Students' League in Mexico-—had attended the Knights of Columbus conference in Philadelphia in February of 1926 in order to lobby for support for the Cristero cause. Later, on their tour of the United States, Capistran Garza and his companions went to the Knights of Columbus headquarters in New Haven to appeal for donations. There, however, they had no more luck than with the bishops: they were brusquely turned away.
"Like the US hierarchy, the Knights were strongly opposed to the anticlerical Mexican government, but the organization's leadership planned to express their opposition exclusively through legal channels. First, they hoped to use their mass membership to put pressure on the Coolidge administration to withdraw diplomatic recognition of Mexico and to lift the arms embargo. Second, they began a campaign to collect donations from KOC chapters nationwide. They then used this pot of money, which they labeled the Million Dollar Fund, to publish pamphlets and other literature about the conflict for distribution in the United States. The KOC leadership in New Haven expressly stipulated that none of this money was to be sent to Mexico, or to be used to finance the Cristero rebellion. As a result the Liga did not receive any funding from the Supreme Council." (Some individual Knights and local chapters did provide financial support, but it was not sufficient.)
(3) Individual wealthy Catholics: "Although the KOC and the NCWC would not back their efforts, Mexican Catholic political exiles had one final avenue to pursue in their search for money and supplies for the Cristero cause: wealthy Catholic magnates. In December of 1926, Capistran Garza met with oil baron William F. Buckley (father of National Review founder William F. Buckley, Jr.) and Nicholas Brady, both prominent multimillionaires sympathetic to the Mexican Catholic cause. He also held a press conference at the Waldorf-Astoria, where he denounced the CaIles government and outlined the main goals of the Catholic activists in Mexico. There, he flattered his American audience. "We millions of Mexicans whose voices are suppressed," he stated, "want you to know that there is a Mexico eager to adhere to and carry out the ideals of liberty that you carry out so gloriously in the United States.". Capistran Garza had reason to hope that this strategy might work. He had received a boost from Wilfred Parsons, the Jesuit priest in New York who used his platform as the editor of the widely read Catholic magazine America to generate public sympathy for the Cristero cause.
"Yet in the end, this strategy proved just as fruitless as the others: Mexican lay exiles were unable to secure significant financial support from wealthy US Catholics. These men certainly had the same concerns as other Catholics about the legality of providing aid to a revolutionary movement. In addition, the US Catholics had become increasingly opposed to supporting either Capistran Garza or the Liga-backed militant movement in Mexico; rather, Catholic leaders, along with the US government and the Vatican, had already "started down the road of diplomatic negotiations." Furthermore, American Catholics were also dissuaded from providing financing to Mexican exiles because of the growing infighting between the political exiles and the Mexican hierarchy in the United States. After 1927, the tension between these exiled factions would become so public that any potential donors were most likely scared away.."