What kind of corporal punishment are we talking about here? It seems to be there are three options:

1) Brief application of pain/discomfort. I.E. Something akin to a severe spanking.
I can't say I see this as being much of a deterrent; spankings didn't really scare me as a kid.

2) Extended periods of applied pain/discomfort.
This runs awfully close to the line of "torture," and I don't think you're going to see any approval for torturing someone as punishment for minor crimes.

3) Brief application of pain/discomfort that leaves long-term physical effects. I.E. Scourging, breaking bones, etc.
This, like (2), is unlikely to get support because it seems to severe for small crimes. Also, the punished individual would likely require medical treatment to prevent infection or deformity and that would have to come out of the state's purse (unless potential death and deformity are to be considered part of the punishment but only applicable to the poor).

I don't see any of these options working out, though perhaps there are others I haven't considered.
Precisely what kind of punishment were you thinking of?
And could you offer some sample crimes that would deserve them so we'll know what level of criminality you're talking about?

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