Perry has dismissed calls to follow two tenets of the federal Affordable Care Act: expand Medicaid, the government program providing health insurance for sick or low-income people, and set up a health insurance exchange where people can shop for coverage.
He has called Medicaid expansion "an unsustainable program" that would cost taxpayers billions.
But protesters on Tuesday told the Fort Worth Star-Telegram said expanding Medicaid would cover more than a million low-income Texans who are desperately in need of healthcare. State officials have previously stated that nearly one in four Texans were uninsured, the highest percentage in the nation.
But the governor has insisted that agreeing to such "Orwellian" programs amounts to making "Texas a mere appendage of the federal government when it comes to healthcare."
Perry is not alone in his position. Other states led by Republicans including Louisiana and South Dakota have also rejected Medicaid expansions. States must expand their Medicaid programs fully to receive federal funding to help enroll newly eligible people.
Recently, however, some Republican governors, including Chris Christie of New Jersey and Rick Scott of Florida, have changed their minds and said they will expand their Medicaid programs using federal money.
Follow Shan Li on Twitter @ShanLi