Maybe a little late to this thread, but here goes anyway...
$66K for a Model S60 still includes a 75 KWH battery that flat out costs Tesla more money. That won't be the case with the Model 3
I would also venture to guess that the profit margin on a base model $35,000 Model 3 with no options will be VERY small if any at all. However, based on prices charged for most options on the Model S, Tesla charges WAY over cost for option items. They're likely assuming that few people will buy a Model 3 without a single option. Selecting just one option puts the company into the plus. $2,000 for Supercharging is pure profit since all they have to do is flip a switch and it's ready to go. Sound studio used be $900, then instantly jumped to $2,500 on the Model S, pure profit. Stock 19 inch wheels ad no cost however the Model S optional wheels are $2,500, yet still 19". Is the alloy on those wheels more expensive than the alloy on the stock wheels? Pure profit. $4,500 for 21" wheels. 95% profit.
Tesla will make a fortune on these cars. Keep in mind they don't have to pay salesman commissions or give up portions of their profits to dealers in general.
The smaller battery, versus the 75 kwh battery in the Model S will likely be around $3,000 less, $6,000 by the time they move battery production into the gigafactory.
$2,000 for supercharging.
Cheaper steel materials plus will be lacking many of the fancy gadgets found in the Model S (Retracting door handles, auto lift trunk, center gauge panel, smaller center screen, minimized interior materials and complexity, probably won't include navigation). Estimating this will save around $5,000 to $8,000.
Likely won't have Brembo brakes which are very expensive, save $2,000 just in brakes alone.
Smaller wheels will save a few bucks.
Model S likely has at least a 10% profit margin built-in to the price for another $6,600.
Many other indirect costs. Naturally, the more you produce of something, the cheaper each unit is. Producing 500,000 cars a year will be much cheaper on a per car basis than producing only 50,000 cars.