The main reason for using rainwater is becaus it contains no minerals such as calcium. The buildup of minerals like calcium cabonate will eventually kill your tree if left untreated.
Putting tapwater outside will not help there. One *could* use demineralized water. Or you could use a rain water collector. Or you could decide to just use tyap water. Then you need to make sure you really put loads of watre on the soil, so that it drains from the drain holes.
If you take tap water, put it in a small bowl, place the smal bowl in a larger bowl and put a lid on the whole thing you'll see water starting to condensate on the inside of the bigger bowl and on the lid. This is evaporated from the smaller bowl and is absolutely mineral-free. You could this way create smaller volumes of clean water if you only have one or two trees (Or use loads of these setups). Natually, you place the setup in the sun for best results.
in any case: A couple of months with tap water should not pose passive problems, except for regions with extremely hard water.