A variable is needed to store the double quote since the action cli command won't let you enter double quotes within double quotes. Also a literal \ is needed when calling the variable so that the it doesn't think your variable name is qpolicy in your action cli command. I believe the actual cli command that runs as a result of the script is (group-policy \policy name with spaces")without parentheses but Cisco appears to not care about the \. Note that after entering this if you perform a show run you will see the command action 103 set q """ As a result, after a reboot this command the """ will not survive and you'll need to enter it again as action 103 set q "\"".
Here is how you do this...
event manager applet test1 authorization bypass
event none
action 101 cli command "enable"
action 102 cli command "config t"
action 103 set q "\""
action 104 cli command "group-policy $q\policy name with spaces$q"