Before I get into that, allow me to contextualize the situation facing Catholic missionaries working in the region. The tasking of converting the indigenous population was hampered by four enormous obstacles: the logistics of evangelizing such a huge population, the cultural divisions that separated the Spanish and Mesoamericans, language barriers, and the massive number of deaths that were sweeping Mesoamerica. The first wave of Franciscans to arrive in New Spain concerned themselves primarily with baptizing natives for the sake of insuring that they died as Christians, rather than instilling them with a deeper understanding of Catholicism. Over time this focus received substantial criticism from other Catholic orders who rightly observed that many of the natives who had been "converted" to Christianity went right back to practicing their traditional religious beliefs once the pressure to convert was taken off of them. Coupled with their experiences from actually working with the indigenous masses, Catholic priests working in Mesoamerica came to realize that they needed to become far more competent in Mesoamerican culture in order to relate Catholicism to the natives in a manner that was relevant to them.

The great irony of Mesoamerican history is that many of our most valuable sources of knowledge were compiled by these early Catholic priests, texts which were prepared largely for the purposes of aiding new priests in their efforts to understand Mesoamerican culture and ultimately destroy Mesoamerican religion. As Catholic friars like Diego Duran and Bernardino de Sahagun researched Mesoamerican history and culture, they quickly came to realize that many indigenous rituals and beliefs were comparable to ones practiced by Catholics. For many Catholic priests, this was proof that natives were in fact a lost tribe of Israel which had gradually distorted their religion over time. Others contended that it was proof that the devil had created a perverted mirror of Catholicism in New Spain which the Catholic God has sent them to destroy. Whatever the interpretation was, missionaries working in Mesoamerica generally tried to avoid making any direct connections between the practice of Catholicism and indigenous religions. There was a strong fear among Catholics working in the region that pointing to analogues between Catholicism and Mesoamerican religion would cause native peoples to fundamentally misunderstand the deeper nuances of Catholicism and in turn lead them to believe that a continuity of their ancient beliefs was acceptable. Serious and often violent measures were taken to destroy all aspects of indigenous religion in order to prevent such an outcome but invariably as the Catholic clergy became better at articulating the breath of Catholicism, indigenous peoples became more aware of the similarities between their belief systems and those of the Catholics and began to selectively adopt and embrace certain elements of Catholicism with zeal, while ignore other facets of Catholicism. Some indigenous groups melded their tradition religious myths with those of Catholicism, others adopted crucifixion as a means of sacrifice, others reworked their religious festivals to appear overtly Catholic, and most adopted local saints as substitutes to their own local teotes.

So to answer your question, Mesoamericans certainly saw a great deal of continuity between their older religious practices and those advocated by the Spanish. Unlike the Catholicism of the period, which had zero tolerance for other religious belief systems, Mesoamerican religion had a long history of blending different viewpoints and practices and so the introduction of new religious ideas was not particularly abhorrent to native peoples. As for the priests themselves, they did not totally avoid relating indigenous ideas to Catholic ones. Practices seen as less threatening to the establishment of Catholicism, like certain dances or asceticism, were begrudgingly integrated and related to by the Spanish but ultimately the Spanish were always on the look out to prevent indigenous beliefs from surviving in a masqueraded form as Catholicism.

EDIT: Re-reading the above, I realize I was a little too general. If you need specifics, feel free to ask.