Temporarily have no gutters, what do I need to worry about?
The biggest concern is definitely leakage and drainage issues. It's hard to say without seeing the property. These may be more or less of a concern depending on the grading around your foundation and your soil type.. not to mention other factors such as the type and condition of that foundation, if you have a sump pump or other drainage system, etc. 

The plants are probably a minor concern, but a hard drip of rain around my house (which does NOT have gutters) causes there to be a break in the vegetation right at the drip line. 

Ultimately, I think you are right to be concerned. If you normally have gutters and even then see water intrusion during heavy storms...well I'd say 1.5" over a few days is moderately heavy!