Hi kittersa,
60Mb is not big. You should see the download bar moving across quite quickly. If not, then close the dialogue box, and re-open. If that doesn't work, then you can just:
1) download from Dropbox to your PC (from the Dropbox website)
2) upload to your website via FTP - put it in the wp-content/updraft folder
If that doesn't work, then you may get some more clues by turning on the 'debug' setting down the bottom of the UD page, clicking 'Save Changes', and then trying again... and then going via FTP into wp-content/updraft and finding the most recent file called "log.(something).txt", and reading that file.
If that's too tricky or doesn't work, you could the FAQs at updraftplus.com, which have the procedure for a manual restore (i.e. not via the dashboard)... if that's too intimidating, then you can try a support package from: http://updraftplus.com/shop/ - the restore package is something like $35, I think.
David