Adjusting that nut should do the trick. You can remove the tailstock from your lathe by loosing the tightening lever and slide the tailstock off the lathe and then set it aside. Next loosen the tool rest base and slide it off your lathe. You can get at that nut easier now. You can also see if there are any other problems with the tool rest base, like cracks or excessive wear. Before putting the parts back on the lathe make sure the ways are clean and not rusted.
If you find the tool rest base is cracked, you can order a new one. The tool rest base for the delta midi model 46-250 is the same as yours and there is one in stock from Sears Parts Direct
http://www.searspartsdirect.com/partsdi ... 217x00001a
Just enter the model 46-250 and then search by model.
Buy a new one only as a last resort. Adjusting the nut should work. Let us know how you make out.