Can my employer take back raises due to an error on their part? Or rather, can they make me pay the difference?

An employer cannot take any amounts out of your paycheck (except taxes and child support) without your written consent.  Further, even with your written consent, the deductions from each paycheck cannot result in your making less than minimum wage for the time period reflected in the paycheck.  You can file a complaint with the Texas Workforce Commission - Labor Law Department (known as a wage complaint or Texas PayDay Act complaint) if the employer makes unauthorized deductions from your paycheck in an attempt to force the repayment of the excess raise. You have 180 days from the date of any unlawfult deduction to file such a complaint. However, be aware that the PayDay Act has no anti-retaliation provisions in it.  So if you are still employed with the employer and you file such a complaint, there is no rule preventing the employer from firing you.  You may get your money back, but you may not have a job either.  Good luck.