"Because after Turbotax did my taxes I owed (and paid) the Federal $46 and I owed (and paid) the State $31 so that total is $77, which is the same amount as the check I received."
That's a coincidence. The IRS has no idea how much you owed and paid separately to the state. (But see VolvoGirl's post below about the possibility that you paid the $46 to the IRS twice and also mistakenly paying the $31 to the IRS instead of to the state. That would result in an extra $77 having been paid to the IRS while also possibly failing to pay the balance due to the state.)
The explanation letter that the IRS issues when they adjust you tax liability generally comes after the check arrives.
Also, check to see if your federal tax return showed an underpayment penalty being included in the amount that you owe. The IRS often calculates penalties differently than does TurboTax based on the timing of the payments received by the IRS.
