Nested IF AND arguments

I'm trying to write a nested IF formula that can return text values based on multiple arguments.

I have a column with dates and I need to know if the date is today, within the next week or within the next month. Then I also need to know if an assigned action has been completed based on a text input column. If the date is today or within a week/month AND the document is with a client, I want it to return 'Due today', 'Due this week' or 'Due this month' as appropriate. 

I have started the following formula but I can't get even the first 2 IF statements to work (due today or due within a week)-
=IF(AND($J79=TODAY(), $H79="With client for approval"), "Due today", "", IF(AND($J79-TODAY()<=7, $H79="With client for approval"), "Due this week", ""))

Error for the code above is 'too many arguments entered'

Any help appreciated