Upgrading to WP 3.7.1 issue

I did a search and looked at some of these…
https://www.google.com/search?q=Could+not+copy+file.%3A+license.txt
…and I do not see any definitive answer anywhere. Do you have FTP (or preferably SFTP) access for performing a manual update?
https://codex.www.ads-software.com/Updating_WordPress#Manual_Update
https://codex.www.ads-software.com/Upgrading_WordPress_Extended

If you can still access your Dashboard, you might try deactivating all plugins and trying the automatic update again, and I would definitely deactivate all plugins before doing a manual update…and if necessary, you can do that by momentarily renaming the plugins folder to something like “pluginsout” and then naming it back.

You can do one thing if you know how to do FTP. You can manually update the wordpress as explained earlier. It seems there seems to be server side issue for copying files. WordPress 3.7 had issue for the HTTPs installation.