Cruz said he was committed to repealing the Affordable Care Act, also known as ObamaCare.

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Cruz’s comments came as Health and Human Services Secretary Kathleen SebeliusKathleen SebeliusSebelius on GOP healthcare plan: 'I'm not sure what the goal is here' Obama's health secretary to be first female president of American University Leaked email: Podesta pushed Tom Steyer for Obama’s Cabinet MORE traveled to Texas Thursday to discuss implementation of the law and its benefits.

“She should hear from the Texas job creators who are facing tough decisions to cut employer hours in order to keep business going and those who simply can't afford to expand their business,” Cruz said.

He said the administration “continues to glaze over the fundamental problems of the law.”

“If ObamaCare is bad enough to delay the pain for big corporations and give a break to members of Congress and their staffs, and too complicated to ensure that people seeking taxpayer-funded subsides are actually eligible for them, then we need to simply do away with it,” Cruz said.

Earlier this week, the administration announced a “fix” to the law, allowing congressional offices to contribute up to 75 percent of employees’ healthcare expenses. Part of the law requires congressional staff to enter into the healthcare exchange system established under the law. And last month, the administration decided to delay the employer mandate requiring businesses to provide health insurance to full-time workers.

Cruz and Sens. Marco RubioMarco RubioRubio defends Trump: 'This whole flip-flop thing is a political thing' Rubio: Shutdown would have 'catastrophic impact' on global affairs Sunday shows preview: Trump stares down 100-day mark MORE (R-Fla.) and Mike LeeMike LeeTrump should work with Congress to block regulations on prepaid cards Sweeping change at DOJ under Sessions Executive orders alone can't create sustainable deregulatory change MORE (R-Utah) are urging their Republican colleagues to reject any federal spending plan that funds ObamaCare, risking a government shutdown this fall. They say it's the best opportunity the party has to stop the law before more provisions are implemented in 2014.

Republicans have argued that healthcare mandates within the law will raise insurance costs for individuals and that employers who would have to provide insurance to full-time employees will reduce workers’ hours and stop hiring.

Democrats point out that the law is already benefiting those with preexisting conditions who can’t be denied coverage, people younger than 26 who can stay on their parent’s insurance plan and women who now pay less for preventative healthcare.