More Ponk channeling! Just kidding Mark!
Don made an interesting comment about dropping the damping factor. I noticed that tubes have a rep for being sluggish but I have found that it is load dependent. A decently done 8 or even 3 watt tube amp into 105dB fairly flat impedance loudspeakers will disabuse any believer in this characterization of tube amps in general. Being "stressed" also affects the harmonic distortion levels as Don pointed out.
So to me, when I think of tube like timbre and tone, I am not thinking of the improperly loaded characteristics of tube amps but rather their low level resolving capabilities particularly the type of zero crossover distortion artifacts (the edginess found in less than stellar SS implementation or PP tubes for that matter). I find tubes more benign in this regard. The commonality for me then of the SS amps I tried with the tube amps I like isn't a warm and fuzzy nature. What they seem to also have in common are very fast switching transistors (look at the bandwidth figures). While these alone are no guarantee of good articulation and by that I mean articulation that sounds natural, I'm just stating an observation.
That said, yes tube amps can be PITAs and like I said, that's why I switched.