Get a date of this week with a name of a day

MyDate.js

function MyDate (args) {
  var MICROSECONDS_OF_A_DAY = 86400000,
      today = args ? new Date(args) : new Date(),
      daysOfThisSunday = Math.floor(today.getTime() / MICROSECONDS_OF_A_DAY) - today.getDay();

  var dayNames = {
    SUN: 0, MON: 1, TUE: 2, WED: 3, THU: 4, FRI: 5, SAT: 6
  };

  return {
    /**
     * @param  {Number|String} day A name of a day OR 0(Sunday),1,2,3,4,5,6
     * @return {Date}
     */
    getDate: function (day) {
      if (typeof day === 'string') {
        day = dayNames[day.slice(0,3).toUpperCase()];
      }

      return new Date((daysOfThisSunday + day) * MICROSECONDS_OF_A_DAY);
    }
  };
}

// With today
var myDate = new MyDate();

var thisMonday = myDate.getDate("MONDAY");
var thisFriday = myDate.getDate("friday");
var thisTuesday = myDate.getDate("TUE");
var thisSaturday = myDate.getDate(6);

// With a specific day
var myDate2 = new MyDate("1978-07-29");

var theMonday = myDate2.getDate("MONDAY");
var theFriday = myDate2.getDate("FRIDAY");

Maybe it's better to make using inheritance from Date.