Need some STM help

TXGalnNYC

Went to my regular checkup today, I am 39.4 weeks along and there has been no change from last week.  Still only 1cm dilated and 50% effaced.   Have any of you STMs been not very far along but still went into labor within the next few days?

 The reason I ask is my due date is Friday and my family is flying in from Texas and they only have a week off work and today my OB offered a membrane sweep but I turned it down and now wonder if I should have done it. 

 Is there still a chance labor could start on its own pretty soon?