Unless there’s a grounding fault somewhere in your house, you should be good. Until tomorrow is probably fine, just make sure that the exposed grounding wire isn’t touching anything conductive in the mean time, and you’re safe even if there is a grounding fault.
If you have a voltmeter, you can measure the voltage between the grounding wire and something conductive that is connected to actual ground, such as a copper pipe or similar. Voltage should be 0 in a healthy electrical installation.
PS: Any tape will do, to be honest, as long as it’s not conductive. The main d9wnside to using duct tape instead of electrical tape is that it’s not according to code, and it looks like ass. But I’ve done it.