In nevada how long is the waiting period to have a response for divorce papers? Do you count the weekends after they are served?

Presuming you mean that a Complaint for Divorce has been properly served, Nevada law provides 20 days to file an Answer, motion to dismiss, or other responsive pleading.  It is calendar days so yes, weekends count, but if the last day is a weekend, you go to the next following work day.  The Complaint should have been accompanied by a "Summons" stating that; if you suspect service was faulty or deficient, you could show the papers you received to a family law specialist who could advise in detail.