I noticed my REUND went down when I entered 2 different Roth IRA's. I input the amount was $2777.78, and I paid Federal Income Tax already of 10% ($277.78). Why do I pay?

While it is true that distributions from a Roth IRA are usually tax free, there are exceptions.  Your distribution is coded as an early distribution with no known exception.  The 10% you had withheld only covers the 10% penalty - it does not cover the regular income tax on your distribution(s).

You stated that you received two identical Form 1099-R's - are these for two separate distributions?  If not, check with your broker about getting corrected forms.

Quick Summary of Roth distribution rules:

• "If you are over 59½, you may withdraw as much as you want so long as your Roth IRA has been open for at least 5 years.
• If you are under 59½, you may withdraw the exact amount of your Roth IRA contributions with no penalties.
• There are special exemptions for first-time home purchase and college expenses."

These facts are from the following link:

http://www.rothira.com/roth-ira-withdrawal-rules 

You can also take a look at the exceptions to early withdrawals at the same link.  After you enter your Form 1099-R(s), Turbo Tax will lead you through questions to see if your distributions meet any of the exceptions to the early withdrawal penalty.