I have made due with a very long large gauge wire from the dryer plug to the welder as well. That will be 20 bucks in cable and a few bucks in ends that I would consider very well spent.
If you have dryer hook ups that usually is sufficient.
Having a previous background in electrical work this is a big no-go. Dangerous and eventually it will bite you in the fourth point of contact. If you're going to go with 220, do the correct thing and get a 220 installed in the garage. That's what I tried to tell you in my post, I don't thing that you can invision how much this is going to run you if you set it up the way I believe you want to. It's not a mere $500.00 and you're set. If you go 220 welder a mid level bender, and get the outlet hooked up, these three issues alone will more than likely run you $2,000 to $2,500. Then of course you have "all" the other stuff. Figure at a minimum of another grand. So I ask you again before you embark on this adventure you may want to make some serious assessments of not only your short term needs of the equipment but more importantly what your needs will be for this equipment in the long run. I as well as more than a few folks on this site I assure you will attest to the fact that they have mucho tools in their stable that they only used once, thinking that they "really" needed them, only to have them sit idle in their tool boxes after that initial use. Heck, I probably got that brand new Dodge Hemi Ram that I want sitting in my tool box.