House Republicans' continuing resolution does not propose defunding the healthcare law, even though the House has voted more than 30 times to repeal or defund parts of the law.
Some Republicans have tossed around the idea of delaying the healthcare law as a way to save money — its most expensive provision, new subsidies to help people buy private insurance — kicks in next year.
But even conservative Republican lawmakers have acknowledged that proposal wouldn't get any traction in the Democratic-controlled Senate and said it might not be a political battle worth waging.
Cruz, though, said the Affordable Care Act will stifle economic growth.
"In my view, Obamacare should be fully repealed, and I have introduced legislation to do so," he said. "At a minimum, however, it should not be implemented at time when our economy is struggling so mightily, at a time when its implementation could push us into a full recession."