Try getting the software (the IPSW file) from another place. Such as here:
http://www.ipadforums.net/ipad-hacking/24939-official-apple-ios-firmware-download-links-ipad.html
Just make sure you download the correct one for your specific iPad.
Don't use Internet Explorer to download it to your computer, use another browser (Firefox, Chrome, Safari, etc). For some reason, IE doesn't play well in downloading IPSWs.
Once you have the iOS, you'll have to put your iPad in DFU mode to use to restore. See this for instructions on DFU mode:
http://www.ipadforums.net/ipad-hacking/27489-dfu-mode-dummies.html
Once you are in DFU mode, open iTunes. It will recognize your iPad as needing recovery. Accept the prompt and you will get the main Summary page for the iPad. Press and hold the Shift key (on a Windows machine; the Option key on a Mac). While holding down the key, click on the Restore button in iTunes.
That should do it. iTunes will start up its magic and, after some prompts, you will end up with an iPad running iOS 6.1.
Yes, it's a bit more of a convoluted way of doing the upgrade - but sometimes, iTunes just can't communicate properly with Apple's servers to get the IPSW in good shape. It happens. This is a way around it.
Good luck and holler back if you need more.
Marilyn