I received a 1099-MISC. My Nonemployee Compensation (box 7) is $1,096.25. It was the only numbered box, 1-17, on the 1099-MISC form. I entered the information on the form into TurboTax Deluxe. It told me that I owed $255 of the $1,096.25 that I made. What are the consequences if I do not claim the $1,096.25? How much trouble could I possible get in for not claiming 1100 bucks?

They will know you did not include it and merely send you a bill for it and a penalty most likely.
If they know you did not include it on purpose, that is tax fraud of course.

I would assume you earned other income . What type of deductions or exemptions are you claiming

It takes awhile, but the IRS does eventually connect Form 1099-MISC income to the tax return.

If it is not reported on the return, they WILL come looking for you.

Trust me when I say that is NOT a pleasant experience.

As AtlantaTaxExpert points out that IRS will certainly find out about unreported Form 1099-misc.

Make sure to report this income. This income is treated as self employed or independent contractor income. You will report your income and expenses on schedule C or C-EZ (Form 1040). This income is subject to SE tax at 15.3%. Read: Your U.S. Tax Return: Tax Filing by Self Employed Sole Proprietor or Independent Contractor