I tried to install a programmable thermostat over the weekend. It is a
one thermostat household with an air & gas furnace set-up (the wires to
the thermostat were W, R, G, Y--I think).

I took the old mercury thermostat off. When I tried to place the new
wires on, after a couple of bad insulation strip jobs, a wire or was to
short to connect. Since this was attached to the heating unit, I
thought I could at least turn it on and get AC until I can get a
professional out to fix the job. When I switched the breakers, nothing
happened. So I tried to put on the old thermostat, but now of a couple
of the wires are too short.

My Question:
Can the professional solder or extend the copper wires to make them
long enough to attach a new thermostat? I ran this by a HVAC tech that
comes well recommended, and he thought he might have to run new wires
from the HVAC units to the thermostat--is this necessary, or can these
wires just be extended from their existing location?