The extension to pay the taxes owed is automatic if you have 2019 federal taxes owed. The taxes owed do not have to be paid until July 15, 2020
However, you still must file your 2019 tax return on or before April 15, 2020 to avoid the failure to file penalties.
When filing your 2019 tax return select the option to pay the 2019 tax with a check. Then continue and e-file your tax return.
Then on or before July 15, 2020 go to the IRS payment website and use Direct Pay to the pay the taxes owed - https://www.irs.gov/payments
An extension is for more time to file, not more time to pay.
So filing form 4868 won't help you.
If you want to wait till July 15 to pay, then wait.
The Treasury Secretary announced that both the filing deadline and payment deadline would be extended to July 15. However, it will take some time to reprogram Turbotax and issue an update. Check the turbotax Coronavirus blog for more info. https://ttlc.intuit.com/community/tax-topics/help/how-are-my-taxes-affected-by-covid-19/00/1330402
For late filing, no program change is required, since the program can e-file up until October 15. You will be past the regular deadline but the IRS won't penalize you. However, if you want an extension to October 15, you probably have to file the request form before the original April 15 deadline.
For late payment, Turbotax can't accept an electronic payment date after April 15, so select "I will pay be check" and then make your own payment arrangements by mailing a check or making an electronic payment at www.irs.gov/payments.