Ok, heres some stuff to clear things up around here. I am somewhat of an amatuer herpetologist and I found this forum by searching for snakes in the Red. Who was it that said Google was a great thing? They were 100% correct.
Copperheads and rattlesnakes both have hemotoxic venom. This, in a nutshell, means that the venom actually begins the digestive process. A mouse or squirrel actually has to worry about their insides being digested, but humans only have to worry about tissue damage. And, if not treated, some bites can be deadly.
However, its important to keep in mind that there has not been a death attributed to a copperhead in more than 40 years, and even the reports of deaths before that are a little sketchy. Most likely the bite was from another kind of pit viper, like a cottonmouth or rattlesnake. Truth be told, most doctors wont even give you antivenin for copperhead bites. Most will just check you out, make sure you're ok, give you some painkillers and antibiotics and send you on your way. Of course, for more serious envenomations, this isnt the case.
Rattlensnake bites should be taken more seriously. While the chances are that the bite victim has plenty of time to get to a hospital, this cannot be guarenteed, and he/she should not waste any time getting to one.
Someone said that a poison control person told them that allergic reactions are highly unlikely. This is not true in the least. I am somewhat surprised that a "professional" would say this. Allergic reactions are actually quite common in snakebites. Alot of experts say that the allergic reaction kills more people than the venom itself.
What Ralst said was good advice and should be taken as such.
About the constricting band. This is good for neurotoxic bites as it helps keep the neurotoxins from reaching the organs. However, in a hemotoxic bite, you do NOT want to keep the venom in one finger or something. Remember what I said about digestion? Believe it or not, you do want the hemotoxic venom to spread a little bit so the tissue damage is less severe in a given area. This, of course, has its exceptions as well.
Sawyer Extractor? Its good for helping keep the victim calm, but to be frank, its almost worthless. You may be able to pull a little of the venom out, but the amount will be almost nil and probably wont make a difference anyways. Dont waste time on it, just get the person to the hospital.
In the herpetology world, there is a big discussion as to whether some pit vipers (which are largely hemotoxic) are developing neurotoxic properties in their venom. The snake most in question is the Timber Rattlesnake. It seems that there have been more and more cases of neurotoxic symptoms in bites from this species, especially in the deep South. Dr. Bryan Frye, probably the worlds most famous and most respected venom researcher, thinks that this venom has been there all along. I agree with him for many reasons...
As far as this happening in copperheads, there have been no reasons, instances, or any evidence that would support such a theory.
Anyways, its midnight and my eyes are drooping. Hope this helps clarify a few things. I cant wait to get down there. Red River Rocks!