I've used Turbotax for years, but they haven't done a great job on this issue. Very frustrating. However, I think I have the answer. Yes, you have to file Schedule H even if you or your payroll company has already paid it. This form shows what you owe, or would owe if it wasn't already paid. Then for the taxes, ss, unemployment, etc. that you've already paid (or that your payroll company charged you for and sent in on your behalf), you have to fill out Schedule 3.
Under Forms, go to Schedule 3. Under Part II, line 8, click on the amount in the right column to bring up the magnifying glass icon. Click on the icon. This will take you to a Tax Payments Worksheet, which is the source of the information for Schedule 3. Your payroll company should/may have provided you with a Schedule H, but it only has the total amount. You'll need to get copies of quarterly reports showing payments made on your behalf. The 1040ES quarterly vouchers only have the total paid, but not enough info which is why you need the reports.
Using the info from the reports, you can now fill out the info on the Tax Payments Worksheet with the date, amount for Federal, and the date, amount, and 2-letter state code for the ID field. The total amount shown on Line 8 (Federal portion) of the Tax Payments Worksheet should match the amount on Line 8a of Schedule H. Line 8 (State portion) of the Tax Payments Worksheet should match the amount on Line 14 of Schedule H. (I don't know if this is the same for all states, but it appears to be correct for Washington...).
So, in summary, Schedule H shows what you owe, and Schedule 3 shows what you already paid. If you paid too much, the overage would be refunded. If you didn't pay enough, the amount you owe is included in your overall tax liability.
Disclaimer: I am not a tax expert - use this info at your own risk. Still, I hope this helps somebody. It took me a while to figure this out. Turbotax should be a little more helpful in the software on this issue.
P.S. I also use SurePayroll. You can find the quarterly reports online under Reports, Quarterly & Annual Reports, 1040-ES, Wage Detail, select the year and click on update. Then just click on View Report for each quarter. I used the 1040ES to find the dates for each quarterly payment on the Tax Payments Worksheet.
