In this paper, we consider the problem of predicting demographics of geographic units given geotagged Tweets that are composed within these units. Traditional survey methods that offer demographics estimates are usually limited in terms of geographic resolution, geographic boundaries, and time intervals. Thus, it would be highly useful to develop computational methods that can complement traditional survey methods by offering demographics estimates at finer geographic resolutions, with flexible geographic boundaries (i.e. not confined to administrative boundaries), and at different time intervals. While prior work has focused on predicting demographics and health statistics at relatively coarse geographic resolutions such as the county-level or state-level, we introduce an approach to predict demographics at finer geographic resolutions such as the blockgroup-level. For the task of predicting gender and race/ethnicity counts at the blockgroup-level, an approach adapted from prior work to our problem achieves an average correlation of 0.389 (gender) and 0.569 (race) on a held-out test dataset. Our approach outperforms this prior approach with an average correlation of 0.671 (gender) and 0.692 (race).