We just bought a new house in June of last year and this is the first time the heater has been REALLY tested (temps in the negatives). Our entire first floor is hardwood or tile with no carpet, but the upstairs is all carpet. We have electric heat and it does come on and heats the upstairs, but no matter what we do, the downstairs won't get above 60 degrees and it's freezing down there. Our living room is a very large, open space and it feels like the heat just can't keep up. The thermostat is downstairs near the living room.

Does this sound like something wrong with the heater or is it just not powerful enough to keep it warm downstairs?

First, it sounds like you should call the HVAC people that did the install. You didn't say if it was central forced air or baseboard so I'll try and address both. If its baseboard first check that all baseboards are on and running. Check circuit breakers and notice if any are tripped. Since you have a thermostat it is most likely central forced air. If thats the case first check the obvious, are the floor vents open and unblocked. You may try and cut back or close off the upstairs vents and force more air out downstairs. Last is the furnace running almost constantly? If so it may well be too small to handle the square footage. Again the HVAC people will figure out what BTU you need. Remember I am just hypothesizing here and good luck!