will need more time to pay my state tax ?

a state extension was probably due 4/15. it does not extend the time to pay a balance due. for that a payment plan is needed. go to your state's department of revenue website to see if they over a payment plan option.  there will be penalties and interest until the balance is paid in full,  

No, if you can't pay, you can set up a payment plan or pay what you can. Extensions are for paperwork, not paying.

There are no extensions for the time that tax due needs to be paid.   If you pay late, you are just late and your state can bill you for interest owed.   Sorry.

You must pay your state tax due using the state’s preferred method of receiving payment.  For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-revenue/L9qVToi02_US_en_US?uid=m6e06um0

WHAT IF I CANNOT PAY MY TAX DUE?

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-payments/pay-taxes/L8aQBCpPO_US_en_US?uid=m9iryksw