No. Pull 'Em tokens do not roll over to the next day.
If you apply a Pull 'Em token to a bet but do not pull a leg before the cut-off time (start of the second half), the token is still considered used. It will not reappear or carry over to future days or future matches.
If your entire bet is voided for any reason, the token will be returned to your account and can be used on another eligible bet.