Both of my neighbors on either side run natural gas, so I assume the lines are close by. My house is all electric and the heating bills are nuts in the winter. I want to look into the cost of putting in a small natural gas furnace and hot water heater. It's a tiny house (around 1,000 sq ft on one level) so I'm thinking I can get by pretty cheap on a furnace (maybe even just a gas powered "wood stove" set in the living room, but the plumbing to run the gas line might be killer. Any guesses as to what it could cost?

I think the gas company will run the line from the main to the meter, which is next to your house.

I had to get me meter upgraded last year.  To pull a new, larger, pipe and install a new meter was $800 IIRC.
That was for a pretty big meter though, so I would imagine, if you don't need that, it would be cheaper.

Um, ask your Gas Co.?

(I'm not trying to be a smart ass but the price can vary from company to company, the distance of the run, right away access, load, etc.)

Figure somewhere between $500 - $1000.

I am also in this situation.  Does anyone know what it would typically cost to pull out the heat pumps and install gas heating?

I would think if your neighbors have NatGas already, the pipe may be underground outside your kitchen door, just not piped into the house

I also assume that you could do the uninstall of the current furnace/A/C units and clear the way for the install of new furnace and exterior heat pump?

if not, your looking at paying labor to tear shit up, which most home owners are quit capable of doing on their own then calling the repair man to fix it