Narratives and studies of Latino partisanship often emphasize Democratic identification, but some have recently suggested a shift towards Republicans. We address these by examining Latino party identification over a 34-year period, leveraging 35 national surveys with a total of over 103,000 Latino respondents along with Census data to create post-stratified survey weights to correct for biases. We emphasize changing partisanship over time by nativity, birth cohorts, and by national origin. From 2000 to 2012, we observed a slight overall increase in Democratic identification and a decrease in Republican identification, but this was driven by foreign-born Latinos. After 2012, we see declining Democratic identification overall, greater Republican identification among foreign-born and older native-born Latinos, and accelerating Independent identification among native-born Millennial and Gen Z Latinos. These results show that generational turnover and differences by nativity challenge extant theories of Latino partisan change over time.