Text visualization and visual text analytics methods have been successfully applied for various tasks related to the analysis of individual text documents and large document collections such as summarization of main topics or identification of events in discourse. Visualization of sentiments and emotions detected in textual data has also become an important topic of interest, especially with regard to the data originating from social media. Despite the growing interest for this topic, the research problem related to detecting and visualizing various stances, such as rudeness or uncertainty, has not been adequately addressed by existing approaches. The challenges associated with this problem include development of the underlying computational methods and visualization of the corresponding multi-label stance classification results. In this paper, we describe our work on a visual analytics platform, called StanceVis Prime, which has been designed for the analysis of sentiment and stance in temporal text data from various social media data sources. The use case scenarios intended for StanceVis Prime include social media monitoring and research in sociolinguistics. The design was motivated by the requirements of collaborating domain experts in linguistics as part of a larger research project on stance analysis. Our approach involves consuming documents from several text stream sources and applying sentiment and stance classification, resulting in multiple data series associated with source texts. StanceVis Prime provides the end users with an overview of similarities between the data series based on dynamic time warping analysis, as well as detailed visualizations of data series values. Users can also retrieve and conduct both distant and close reading of the documents corresponding to the data series. We demonstrate our approach with case studies involving political targets of interest and several social media data sources and report preliminary user feedback received from a domain expert.