There is no reason you can't do a self supported TA with your current bike and a small amount of inexpensive gear. I have gone with a variety of gear and a variety of packing styles. If you don't go crazy buying high end gear you can go much cheaper self supported rather than credit carding it. I have met folks touring with only very inexpensive gear and they were having as much fun as anyone.
John's estimate of motel costs is conservative and as he said you can buy a lot of gear for $3500. It is definitely possible to buy everything including the bike, pay airfare to and from the trip, and cover food and camping fees and stay under that amount. If you are really frugal you could do it for way under that amount.
Take only what you need and the rack and panniers you have are probably adequate. You can put a bar roll on the front and strap the tent on the top of the rack to stretch capacity a bit. It is pretty easy to get packed weight down to 30 pounds and 20 pounds isn't crazy light.
I'd suggest you buy a fairly inexpensive tent like maybe a Eureka Spitfire 1 ($140), use a pop can stove, and pick a sleeping bag and pad that suits your budget. You can get by with a $12 foam pad and a $70 sleeping bag or you can splurge on nicer stuff. I used a cheap bag and an old thermarest on the TA (my first tour), but later splurged on a real nice bag and a NeoAir pad. I like the nice $$$ pad and bag, but was OK with the cheaper stuff.
The bottom line is that you can tour with $200-300 of gear or you can spend a lot more. The thing is that the folks I met going really cheap seemed to be having as much fun as the folks that dropped a bundle of gear.
Camping on the TA can easily average <$5 per day without too much effort to go cheap and some have managed $0 per day.
Eating can be cheap or expensive depending on your choices. I like to cook dinner in camp, but often eat breakfast or lunch in a diner or restaurant.
I wrote a couple articles that might help. Check them out at:http://www.crazyguyonabike.com/doc/frugalhttp://www.crazyguyonabike.com/doc/Ultralight