Warning: Contents of this paper may be upsetting. Public attitudes towards key societal issues, expressed on online media, are of immense value in policy and reform efforts, yet challenging to understand at scale. We study one such social issue: homelessness in the U.S., by leveraging the remarkable capabilities of large language models to assist social work experts in analyzing millions of posts from Twitter. We introduce a framing typology: Online Attitudes Towards Homelessness (OATH) Frames: nine hierarchical frames capturing critiques, responses and perceptions. We release annotations with varying degrees of assistance from language models, with immense benefits in scaling: 6.5x speedup in annotation time while only incurring a 3 point F1 reduction in performance with respect to the domain experts. Our experiments demonstrate the value of modeling OATH-Frames over existing sentiment and toxicity classifiers. Our large-scale analysis with predicted OATH-Frames on 2.4M posts on homelessness reveal key trends in attitudes across states, time periods and vulnerable populations, enabling new insights on the issue. Our work provides a general framework to understand nuanced public attitudes at scale, on issues beyond homelessness.