Cornyn's comments came a few hours after the Supreme Court handed down its ruling that the healthcare law is constitutional. The court notably upheld the much-criticized individual mandate provision in the law.

"What it has clarified is the importance of the election on Nov. 6, 2012," Cornyn said. "The only way to stop the overreaching by the federal government, including the president's flawed healthcare bill, is to elect a new president and a Congress that will repeal and replace this fundamentally flawed law.

"Before the healthcare bill became law, the president repeatedly assured the American people that he would not raise taxes on the middle class. He declared emphatically that the individual mandate was "absolutely not a tax increase," but the Supreme Court of the United States has made absolutely clear that the only way ObamaCare can be upheld as within the constitutional power of Congress is for it to be considered a tax increase."

The best way to improve the healthcare system is not through the Obama administration's healthcare law but through "patient-driven reforms," Cornyn said.

"ObamaCare increases the cost. We need to reduce the cost and make it more affordable," Cornyn said. "And the best way to reduce cost is through patient-driven reforms that increase transparency, eliminate government distortions and boost private competition. Those are the reforms that Americans want and those are the reforms that they deserve."