Based on the procedure described in Pub 17, it seems my tax due should be much more that what the program put in. Line 15 of 1040-SR is slightly over $201,050, but the tax due is like it was $150,000 (-ish)
It depends on what kind of income you have. There are like 7 different ways to figure the tax.
See the IRS worksheet on 1040 page 36 for how the tax is figured. Turbo Tax uses the same worksheet.
https://www.irs.gov/pub/irs-pdf/i1040gi.pdf
Even though it shows up as income on the first page,if you have capital gains or qualified dividends the tax is not taken from the tax table but is calculated separately from schedule D. The tax will be calculated on the Qualified Dividends and Capital Gain Tax Worksheet. It does not get filed with your return.
In the online version you need to save your return as a pdf file and include all worksheets to see it.
For the Desktop version you can switch to Forms Mode and open the worksheet to see it. Click Forms in the upper right (upper left for Mac) and look through the list and open the Qualified Dividends and Capital Gain Tax Worksheet. And you will need to use this IRS worksheet on page 15.
If you haven't yet finished and paid, and are using Online TurboTax, here's a way to see the method(s) that TurboTax used to figure your tax.
If you are using desktop TurboTax, you can go into Forms Mode and view the Form 1040 Worksheet (Wks).
On that worksheet scroll down to between Lines 15 and 16 and view the Tax Smart Worksheet which will show what methods were used.