If one overpays the state income tax, they receive a 1099-G the following year for the refund amount. This makes sense since  you were able to deduct all that was deducted rather than just what was ultimately owed. If your highest tax bracket didn't change from one year to another,  it is pretty much a wash. 

However, now that the state income tax is limited, you may not be able to deduct all the state income that was deducted. If you then receive a 1099-G, you will be including income that was not deducted the previous year. Let me use an example to hopefully make clear what I am trying to say (Property tax kept out of this for simplification)

2018 - total state income deducted = $12,000. You are able to deduct only $10,000 for the 2018 tax year. After you complete your state returns, it is determined that the state tax due is $11,000.   You overpaid by $1,000 and that $1,000 is given to you as a refund. If we are playing by the old rules, you will receive a 1099-G for $1,000 to be included as income for 2019 tax year. Did you just get hosed? You paid $11,000 in state taxes, deducted $10,000 in 2018, and received a 1099-G for $1,000 (which will be added to your income next year). 

Let's say you only had $10,000 deducted for state taxes. You deduct the entire $10,000. Turns out you owe an additional $1,000. That's fine, you write a check to the state for $1,000.  You are still paying the same $11,000 to the state as the previous example but next year you don't get the $1,000 1099-G. It sounds to me like you come out ahead this way. If this is right, lesson learned, don't overpay state income taxes.