Our federal and state refund dropped $1,200 when my self-employment taxable income was added at $1,900. What could be causing me to be taxed this much?

There are a few possibilities.  

1. Your Self-Employment tax is 15.3% of that $1,900 so $290 would be added to the tax you owe.
2. Depending on how much other income you had, you may have qualified for a credit you no longer qualify for, if you were right on the cusp of not qualifying.  
3. You jumped  tax brackets with the additional income causing some of your income to be taxed at a higher rate.

You can look at your 1040, write down all the numbers then remove the income and look at your 1040 again and compare where the changes are coming from.  Then once you compare remember to re-enter the income from self-employment. 

You can see your 1040 using forms mode in TurboTax Desktop or if you are using TurboTax online by clicking the following:

• Tax Tools
• Tools
• View Tax Summary
• Preview My 1040