If you have the ends of two wires, you can't possibly be measuring
amps. So either you are completely confused, or I have completely
misunderstood what you are talking about. Amps are what you get when
electricity travels through things. If there is no _thing_, then there
are no amps. What you said is basically the same as me saying "I walked
out to the road in front of my house with a meter and measured 35mph
coming out of the road." It just don't make sense.
What you likelly have is not 122 volts. What you have is 12V. There is
a transformer in your basement that converts from 122 volts down to 12.
Now, this transformer is only capable of putting out a certain number
of amps, maybe just 1 or probably even less (I really don't know -- but
it is certainly down in the range of a few tens or hundreds of
milli-amp, and not more than say 1-amp). When you put your "2-amp"
thermostat on, it tries to pull too much electricity through the thing.
What ends up happening is that the transformer can't keep up, and could
overheat and ruin itself. In these cases you might see the voltage drop
below 12V, and you would inteed get a "low power" indicator. Of course,
you won't see any such drop when there is no thermostat connected.
Alternatively, is it that you only have a _single_ wire, which you are
measuring the current as it is travelling through the wire? In that
case you could be trying to wire something in series (where I mean
_really_ in series, electrically, not as many people use the word).
Which is bad.
Or I could just be completely off my rocker. (Admittedly, I haven't
slept in a bit.)