Did you leave the lathe with the Delta repair center? (Even though they can't look at it for a week or more, if it's broken there's not much you can do with it anyway.)
Be persistent -- gentle, but persistent. It's failed within the warranty period, it's their job to fix it or replace it. Insist.
Another thought -- where did you buy the lathe? And did you pay using a credit card?
If it's a walk-in store, the shop manager might help you, especially if you gently suggest that this will be a factor in whether you feel loyalty to the store in the future.
Credit card companies often offer "extended warranty coverage" -- sometimes a year beyond the manufacturer's warranty. Check the invoice and receipt to see how it was purchased, and if it was a CC, check with the card company's customer service department to see if they can help.
Hope some of this helps and you soon get back to turning happily.