I ASSUME you are talking about stock options for employer stock, not "exchange-traded" options.

To be clear, you don't sell "stock options" in this situation, though you might sell the stock acquired via the exercise of these options. 

ASSUMING the options are non-qualified options then it's the EXERCISE of the options, reported as compensation, NOT any "sale" of the stock, that's the income event.  You might sell some or all of the stock simultaneously with the exercise in order to fund the exercise and/or in order to fund the withholding taxes required because of the EXERCISE.  The sale itself in this situation creates no income, it might create a small loss.  But there WILL be income tax withholding and that income tax withholding should, more or less, pay the necessary taxes.  (As always when dealing with taxes, the devil is in the detail, but typically there's no need to make an estimated tax payment.)

ASSUMING that the options are qualified option, then the exercise itself will not be an income event.  Again, you might simultaneously sell some or all of the stock acquired and if you do that the sale in this case will trigger income, but it will also be considered compensation to be reported on the W-2 and the fact that compensation is reported means that withholding will be required which means that some of the cash generated by the sale will go back to the employer who will pay the government.  So, again, that income tax withholding should, more or less, pay the necessary taxes.  (As always when dealing with taxes, the devil is in the detail, but typically there's no need to make an estimated tax payment.