Why is my heat pump blowing cold air?
I believe it's easiest to say that you need to get an HVAC maintenance company to come check on it. The auxiliary heat is entirely separate from the heat pump, that is why it's also used as an emergency system.

However, how cold has it been recently? A heat pump will only work to around 34 degrees or so outside and then it should switch off and allow the auxiliary to heat the home alone. Without going into too many details about the various possibilities, it could be that it's too cold outside for the heat pump, but the auxiliary isn't taking over (an issue with the thermostat and it's wiring to the system.) In regular heating mode, your heat pumps runs until it's too cold outside, and then the auxiliary takes over. In emergency heating, the auxiliary runs only. However, if it's been below say 34 degrees for those last two days, then your auxiliary would have been running entirely anyway and you wouldn't be saving any.

Again though, it's an advanced system and this could be caused by multiple issues - have someone come look at it.