Yes, it is possible. I know of two professional shops that use NG for their forges. One is in Phoenix and the other is in NYC. You CANNOT use standard propane burners with natural gas. That will cause an explosion hazard. The orifice size on the burners is different for LPG and NG. They also operate at different PSI (IIRC)

I would not recommend trying to do this without getting the correct burners and some professional help.

Is it possible to use the natural gas coming to my house

 Possible... yes, Practical.... no.

The typical pressure that residential NG is around⁢ 7 inches ‍of water column ⁤(WC), equivalent to about 0.25 ⁤psi (pounds per square inch)

One cubic foot of propane = 2,516 BTUs compared to one cubic foot of natural gas = 1,030 BTUs. Propane contains more than twice the energy of natural gas. In one hour, a 100,000 BTU natural gas furnace burns around 97 cubic feet while a propane furnace burns only 40 cubic feet in an hour.

What that means is for NG the pressure (PSI), used at the endpoint... as in a forge burner, needs to be double or more of what PSI a propane burner requires.  Example:  If a given venturi burner forge, which uses a single burner requires 15psi, you'd need AT LEAST 30psi of natural gas. That's just not going to happen with a residential Natural gas supply/service.  

 To get that, it would require a new service to be installed, IF laws/statutes in your local would even allow it. 

  Even though propane sounds like an expensive venture, it is far simpler and far cheaper to install vs Natural gas using a residential source.  

  I installed my piping throughout my shop, dug the trench from my shop to where I wanted the propane tank, (in my area the tank is required to be buried, at least 25ft from the structure). 

   When the propane company showed up with the 500gal tank....they placed it, and then pressure-tested the piping I installed.  When my piping passed the pressure test (1 hr at 100psi with no drop), the propane folks installed the last connection to the tank using 0-50psi adjustable regulator. 

  My cost, to the propane company, was a $50 annual tank rental, and the cost of filling the tank.... at that time, if memory serves, was about $1,1000 give or take. 

  I have 3 forges in my shop, and keep the tank regulator set at 40psi.   Maintenance usually consists of me knocking a wasp nest out of the tank's connection cover once or twice during summer.  😉