What you are calling FICA tax is self-employment tax. It's included in the total tax on your federal tax return. You don't pay it separately.
You can cover the tax on your self-employment income (i.e. freelance income) either by making an estimated tax payment or by your spouse increasing withholding for the rest of the year. Either way there should be no penalty. If you make the estimated tax payment you might have to make some extra entries on your tax return to avoid a penalty, but if the amount is small it might not matter. Using withholding will definitely avoid a penalty. You can use the Tax Withholding Estimator on the IRS web site to figure out what your spouse should put on the W-4 form. The estimated tax or withholding covers all the tax on your federal tax return, including the self-employment tax.
New York City tax is included in the total tax on your New York state tax return. You don't pay it separately.
