Developing machine learning models to characterize political polarization on online social media presents significant challenges. These challenges mainly stem from various factors such as the lack of annotated data, presence of noise in social media datasets, and the sheer volume of data. The common research practice typically examines the biased structure of online user communities for a given topic or qualitatively measuring the impacts of polarized topics on social media. However, there is limited work focusing on analyzing polarization at the ground-level, specifically in the social media posts themselves. Such existing analysis heavily relies on annotated data, which often requires laborious human labeling, offers labels only to specific problems, and lacks the ability to determine the near-future bias state of a social media conversations. Understanding the degree of political orientation conveyed in social media posts is crucial for quantifying the bias of online user communities and investigating the spread of polarized content. In this work, we first introduce two heuristic methods that leverage on news media bias and post content to label social media posts. Next, we compare the efficacy and quality of heuristically labeled dataset with a randomly sampled human-annotated dataset. Additionally, we demonstrate that current machine learning models can exhibit improved performance in predicting political orientation of social media posts, employing both traditional supervised learning and few-shot learning setups. We conduct experiments using the proposed heuristic methods and machine learning approaches to predict the political orientation of posts collected from two social media forums with diverse political ideologies: Gab and Twitter.