State extension payments made in 2018 for 2017 were unnecessary. How can I net the full extension payment against the refunds reported on 1099-G?

By "extension payment" do you mean you filed for an extension for filing a state return and are making a payment with the extension form?  Have you already made the payment?

In 2018, I filed for extension for 2 -2017 sate returns and made an extension payment with each.  Because we are cash basis, I did not take a deduction on my 2017 federal return for the payments made with the state extensions.  When I input the payments as payments in 2018 for 2017 and also report the full refunds from each state, The Form 1040, Line 10, "State and Local Income Tax Refund Worksheet takes my input and treats the payments made in 2018 for 2017 as if they were paid in 2017 and included in the State income tax deducted on Schedule A on my 2017 return.  They were not included in 2017 itemized deductions because the payments were made inh 2018.

This seems like the same problem I'm having with one state return. Extension payment for 2017  $ 4000 paid  in 2018, refund $ 6842, Turbo tax says $ 5322 taxable, but I thought it should be $ 2842. We itemized on 2017 return and didn't on 2018. TT questions just ask how much was paid with extension but NOT when it was paid.

YES!  This is the same as my problem!  I have verified that the 2017 Extension Payments Made in 2018 are in the correct column on the calculation worksheet, however, the form then seems to assume that those payments made with the extensions were actually part of the taxes PAID in 2017 and included on the 2017 Schedule A.  Do you think it is a TT bug?

Are you preparing the 2017 or 2018 return?  Since the payments were made FOR 2017, enter them in your 2017 return, even if your business is on a cash basis.  [It's similar to the Q4 estimated payment being made in January of the following year.]

I am preparing my 2018 return.  I am not preparing for a business, I am preparing our personal return.  The problem is that TT is calculating that I should pay tax on nearly 100% of the refund received.  I'll go to the IRS website and their forms and instructions.  

No -- You can't net the amounts.  They are reported in different places in the program (and on the state returns).  The IRS and the states are going to be looking to match the amounts entered on the 1099G forms.

To get the same effect, however, what you can do is to make sure you report the payment made with your extension.  To do this, please follow these steps:

1. Click Federal Taxes > Deductions > I'll choose what I work on
2. In the Estimates and Other Taxes Paid section, click on the Start/Update box next to Other Income Taxes.
3. Click the Start box next to Payment with 2018 state extension.
4. Click Multiple States from the drop down list.  [It's the last item on the list.]
5. Put the total amount of all state extension payments.
6. Then go to each state return and enter the extension payment for that state.
   

I don't see how to do the last step in the program. When I go to state estimated payments it tells me to go back to federal to put in the amount. But if I have multiple states, it says to do it in each state.