Just for the record here, Drafts includes the Date.js library in it’s Javascript runtime automatically, so Date.parse is dramatically enhanced over the standard Javascript version.
A few examples:
Date.parse("t") // Returns today's date.
Date.parse("today") // Returns today's date.
Date.parse("tomorrow") // Returns tomorrow's date.
Date.parse("yesterday") // Returns yesterday's date.
Date.parse("next friday") // Returns the date of the next Friday.
Date.parse("last monday") // Returns the date of the previous Monday.
More examples in the Date.js read me.