Move in? what's happening at the house now?

Are you saying that it was $30 with no lights, heat, etc, but now $158 now that the builders have turned the lights and heat on?

I certainly don't think $150 to heat a house in January in N. Ohio is out of line - in fact most people would be pretty happy about that. That was about my bill in NC (although bigger house). Mind you 58 degrees is pretty chilly - so you are probably going to be $200 at 68. That is still considered normal.

I am thinking weed is right.

You may not be as "well insulated" as you thought but really those numbers are not out of line. It is really your propane cost that is going to hurt.

I would suspect that average home at 2800 sqft in N Ohio without NG access is probably $1700 a winter. Being new, you are probably going to be $1300. $200 electric, $200 propane in Jan. is about right. I am just throwing out numbers of course.

Something to consider - is the propane turned on or is your heat pump just doing all the work? Certainly it has been below 30 degrees. And another thing - all sorts of stuff happen during construction. Like electric heaters, windows left open etc. Did your hot water heater get turned on also?

It sounds like the billing period included the first time the HVAC was turned on for the new construction. A lot of that bill might be just the initial cost of warming up the structure, and not an indicator of ongoing heating cost. Realize the thermal mass of the house is way, way more massive than just the air in the building envelope. If the structure was stable at an ambient temperature more like the outdoor temp, then it'll take quite a lot of initial heating to get that up to the 58 degrees.

I kind of remember this from a a few years ago when we moved into our remodel three days before the utility turned on the gas, coincidentally also the coldest day that December. The first day we finally got gas hooked up, the furnace was running a lot higher than any normal day, because all that heat was being absorbed into the walls/studs/floor/tile/etc.

If you were doing that initial warm-up with a heat pump in 30 deg temps, I could see where it would take even longer and cost quite a bit more.

Sounds like the construction workers were having their way with your system while unsupervised.

The construction dust may have clogged up the filter.

Heat pumps often are installed with auxiliary electric strips for providing emergency heat to cover unit failure and supplemental heat to cover cold weather below the design point of the system. Turning on the electric strips can be controlled by the thermostat, perhaps when the set point is raised more than, say, two degrees above current temperature. It might be set up to go to auxiliary when the heat pump by itself is taking too long to bring up the temperaure. It also can be triggered by an outside temperature sensor. It all depends on how the system has been set up.

As others have pointed out, the electric bill may not be unreasonable for a winter month, but if it really is higher than it ought to be then it could be that those backup strips are coming on when they shouldn't be, in which case the thermostat setup ought to be reviewed. You can look up the details of your thermostat controls online and see for yourself how it might be set up.

If your backup heat system is propane, then perhaps you should check to see if the electric strips, if present, are enabled or not. There would be a separate breaker in the panel for that, as the current draw would be quite high.

$158 sound very reasonable for winter months. It cheap!