Is there anything I can do to receive STD benefits for my pregnancy before my 60 day LTD elimination period ends?

I had a long term disability (elimination period 60) with UNUM till May 2013 and this year (starting June 2013) I chose the short-term disability (elimination period 0 days). I had a baby two weeks ago and was told by UNUM that I am covered under the Long Term Disability because when I got pregnant I had that policy and not the new one. I was not aware of this condition in the policy and I was wondering if there is anything I can do to receive the STD benefits before the 60 days. I had a C-section and will be out from work for 8 weeks (which is less than 60 days). Thank you.