Although there exists a large sample of known exoplanets, little spectroscopic data exists that can be used to study their global atmospheric properties. This deficiency can be addressed by performing phase-resolved spectroscopy -- continuous spectroscopic observations of a planets entire orbit about its host star -- of transiting exoplanets. Planets with characteristics suitable for atmospheric characterization have orbits of several days, thus phase curve observations are highly resource intensive, especially for shared use facilities. In this work, we show that an infrared spectrograph operating from a high altitude balloon platform can perform phase-resolved spectroscopy of hot Jupiter-type exoplanets with performance comparable to a space-based telescope. Using the EXoplanet Climate Infrared TElescope (EXCITE) experiment as an example, we quantify the impact of the most important systematic effects that we expect to encounter from a balloon platform. We show an instrument like EXCITE will have the stability and sensitivity to significantly advance our understanding of exoplanet atmospheres. Such an instrument will both complement and serve as a critical bridge between current and future space-based near infrared spectroscopic instruments.