"What they actually did was they corrupted my bill to have the secretary just say, 'Oh, yes, she can certify that there's some sort of a program there to verify the income,'" Black told the Fox Business Network.
"We know this system's not working, and now we're going to trust the secretary? We just have a train wreck as a result of what she's put forward. And there's going to be terrible fraud and abuse [in] this program because of that."
Under the health care law, all individuals who are not already covered are required to purchase health insurance, or else pay a fine to the government. But to assist in the cost of health insurance, the federal government is providing tax subsidies based on income.
Republicans have expressed concern that individuals applying for the subsidies could underestimate their incomes to receive more generous government benefits.
Under the agreement signed by President Obama on Thursday, the Department of Health and Human Services is required to provide Congress with a pair of reports addressing the income verification issue.
One will show how the government plans to ensure that those who sign up for the exchanges do not lie about their income levels. The other will detail an inspector general's report on safeguards available under the Affordable Care Act for fraud reporting.
Black called the implementation a "train wreck" and said she was not confident the government would be able to properly administer enrollments.
"It's a mess," she said.