Nope...when you book over the phone your airfare is guaranteed until midnight, your local time, the day you call--the seats are held from inventory 'til midnight the following night. Once you pay for the ticket over the phone on a non-refundable ticket, you have 24 hours in which to get a no questions asked refund under the guidelines of "Our United Committment." After the 24 hours is up, you're stuck with the ticket.
As far as getting the DEN staff, call 1-800-225-8900 and 95 times out of 100 you'll get DENRR.