Taking turns speaking in front of the Texas Capitol on Wednesday, a group of critics of the federal Affordable Care Act focused most of their comments on a fellow opponent of the health care law: U.S. Sen. John Cornyn.

Last month, Cornyn, the Senate minority whip, withdrew his signature from a Republican-drafted letter that demanded Congress defund the health reform law as a condition for supporting the entire budget.

On Wednesday, a half-dozen speakers with the "Exempt America Tour" — which included Tea Party members from across the state — repeatedly called on Cornyn “to join the fight,” and praised the likes of his Republican colleague, U.S. Sen. Ted Cruz, for leading the charge against the law, commonly known as “Obamacare.”

“He is one of those who has been so outspoken in his opposition to this,” Brent Bozell, chairman and co-founder of ForAmerica, an online conservative movement, said of Cornyn. “He has spent so much time telling the voters of Texas how he was doing everything in his power to put an end to it. So far, he’s ducking.”

Jessica Sandlin, Cornyn's Texas press secretary, said that the senator has been fighting Obamacare for four years, and is an original co-sponsor of Cruz's legislation to defund the measure. "He voted against Obamacare repeatedly before it became law and he’s voted to fully defund and repeal it every time it’s come up for a vote," Sandlin said.

The speakers at Wednesday's event also talked about why Congress should exempt all Americans from Obamacare. The law marks a major milestone Oct. 1, when online health exchanges, allowing the uninsured to shop for health coverage, will take effect.

“We’re here to tell them get some courage, at least honor your promises,” said Tonya Robertson, a Houston-based Tea Party state coordinator.

Robertson said that her family was considering dropping their health insurance. She blames Obamacare for increasing their premiums and deductibles in return for less coverage.

Earlier this month, Obama approved a decision by the Office of Personnel Management to allow the federal government to continue subsidizing health plans for all lawmakers and their staffs.

“If the law isn’t good enough for our lawmakers, the law isn’t good enough for my family or any family in America,” Robertson said.

“It’s time for Republicans to get a backbone and stand with us and fight back,” said George Rodriguez, a San Antonio Tea Party coordinator. “If we lose this one, we’re going to lose America.”

In the next week, the group of speakers will be making stops in Mississippi, South Carolina and Virginia.

This story was produced in partnership with Kaiser Health News, an editorially independent program of the Henry J. Kaiser Family Foundation, a nonprofit, nonpartisan health policy research and communication organization not affiliated with Kaiser Permanente.