The software gives you the option to select liability in 1 year or 3 years, but doesn't change the calculated tax that I owe with either option.
No you do not have that option. TurboTax is only calculating tax on the 2020 1/3 portion. The remaining 2/3 will be taxed at your 2021 and 2022 marginal tax rates. With 2/3 of the distribution deferred to 2021 and 2022, you have options to repay a portion or all of the distribution amount attributable to those years. Any repayment would decrease the amount of tax you owe on the remainder of the 2020 Covid distribution. Additionally, this amount will taxed at your marginal tax rate in 2020 and 2021 so the next two years you do not want to add additional income to your return that might push you up into a higher tax bracket.
The 8915-E will be used for penalty relief from early retirement plan distributions and include the option to spread the distribution income over 3 years. This is a good option if the distribution is pushing you into a higher marginal tax bracket for 2020. You may end up paying less tax if you spread the distribution over the 3 years
Even though TurboTax Desktop goes through and shows that we took the 3 year repayment option, at the end of the Federal Tax section, it shows us owing taxes on the FULL 2020 IRA distribution.