Nobody except for Steam's (Valve's) employees knows for sure. In past years, Steam has held two big sales per year: the Steam Summer Sale and the Steam Holiday Sale. In past years, the summer sales has usually begun on the last Thursday in June.
Unfortunately the prediction of a July 4 date for the Steam sale didn't come true but that's ok because new reports suggest that the sale is approaching sooner than you think. RELATED: Steam Summer Sale 2013 Date Leaked? Rumors Suggest July 4 Start Date; See Full Game List Leak Here.
Update: A Valve rep has confirmed that the date indicated by PayPal is correct: The Steam Summer Sale will begin on June 22. Original story: The Steam Summer Sale dates have been revealed, and once again we have PayPal to thank.