The 20 days means 20 calendar days, which would include weekends. However, there are certain major federal holidays that are not counted. Also, if the 20th day falls on a Saturday or Sunday, then the deadline is the next business day, or the following Monday.
Generally though, it is best not to wait until the very end of the 20 days to respond in order to avoid a potential default. Typically, the Answer to the Petition should be RECEIVED by the clerk of court in the county where the petition was filed no later than the 20th day. However, if for some reason you have missed the 20th day, you should immediately file a motion to set aside default and request a hearing so that your rights are protected and your position on any and all disputed matters can be heard.