I have opted to pay my State Tax using IRS refund via auto transfer. Fed return is taking longer. NY state tax dept is asking to pay soon.What can be done here?

PAY IT ASAP to stop the penalties/interest from accruing further ...  you can NEVER EVER  have a state balance due  paid with a federal refund ... that was NOT an option in the program.  What you may have seen is the "summary" screen showing you the net result  between the fed refund and the state balance due. 

Check the printout or PDF of your return; look for the state cover sheet with the Turbotax logo. If you owed tax, it will show the payment information and how/when you decided to pay. Read the state payment instructions carefully since most states cannot be paid from within the TT system and requires additional steps.
https://ttlc.intuit.com/community/refunds/help/what-are-my-options-for-getting-my-state-refund-or-fo...

No, you misunderstood. That's not possible. You might have had the Turbo Tax fees deducted from your refund.

The state tax can not be deducted from the federal refund. NEVER. You can only have the Turbo Tax fees deducted. You will still get the full federal refund minus any fees you had deducted. Turbo Tax just shows you a screen at the end showing the Net amount of federal and state combined. But it is just for your own info. You do still have to pay the state yourself separately. See,
https://ttlc.intuit.com/community/state-taxes/help/can-i-pay-my-state-taxes-from-my-federal-refund/00/26288