In Drupal 7, how do you git clone a module project quickly?
Just use the format you say doesn't work. This is the correct format. The URL does matter. (Do not use the format that produces the error.)

I.e. to clone branch 7.x-1.x of tb_megamenu, you should use:

git clone --branch 7.x-1.x http://git.drupal.org/project/tb_megamenu.git


You may skip the --branch option and branch identifier when cloning.  This will clone the current HEAD, which may (or may not) be the head of the branch you want.