For federal estimated tax payments, Social security - yes. State taxes - No.
When you are self employed, part of your tax due will be for self employment taxes, which are Social Security and Medicare. When you make the estimated tax payments, these payments are applied to both your SE taxes and your income taxes.
For your state taxes, you can make separate estimated tax payments for your state. TurboTax can walk you through this during your state interview. There will be a question towards the end of the interview that ask if you want to prepare estimated state tax payments. You can also find information on your states tax website about making estimated tax payments.