The nature of the progenitors of Type Ia supernovae (SNe Ia) is still a mystery. While plausible candidates are known for both the single-degenerate and double-degenerate models, the observed numbers fall significantly short of what is required to reproduce the SNe Ia rate. Some of the most promising single-degenerate Type Ia progenitors are recurrent novae and super-soft sources (SSS). White dwarfs (WDs) with higher mass transfer rates can also be SN Ia progenitors. For these rapidly accreting white dwarfs (RAWDs), more material than is needed for steady burning accretes on the WD, and extends the WD's photosphere. Unlike SSS, such objects will likely not be detectable at soft X-ray energies, but will be bright at longer wavelengths, such as the far-ultraviolet (UV). Possible examples include LMC N66 and the V Sagittae stars. We present a survey using multi-object spectrographs looking for RAWDs in the central core of the Small Magellanic Cloud (SMC), from objects selected to be bright in the far-UV and with blue far UV-V colors. While we find some unusual objects, and recover known planetary nebula and Wolf-Rayet (WR) stars, we detect no candidate RAWD. The upper limits from this non-detection depend on our expectations of what an RAWD should look like, as well assumptions about the internal extinction of the SMC. Assuming they resemble LMC N66 or fainter versions of WR stars we set an upper limit of 10-14 RAWDs in the SMC. However, our survey is unlikely to detect objects like V Sge, and hence we cannot set meaningful upper limits if RAWDs generally resemble V Sge.