I would wait the week or so to get new filters before going to other sources, but distilled definitely could work. But as Dan said, could get pricey fast...
Option two, depending upon what is wrong with your RODI machine you could
1) If it's the RO membrane, then run water through the prefilters (carbon is the big one to dechlorinate it) and then through the DI resin... but you'll burn through resin quickly
2) If it's the DI resin, skip that step, a few TDS ain't going to hurt
3) If it's both the RO and resin, run it through the prefilters, assuming you are getting municipal water and not well water then the TDS shouldn't be a huge issue for one water change or fresh water top off.