The issue on which Cruz has been most clear and forceful lately is an effort to defund Obamacare that has gained little traction. He is pushing a plan that Sen. Mike Lee (Utah) circulated in July calling for Republicans to refuse to support any continuing resolution or appropriations bill that would fund the health-care law. The current funding measure runs though Sept. 30, meaning the government will shut down after that if Obama does not get a new bill.
This is the sort of tendentious lying that has made the Washington Post a byword in liberal fascist propaganda hackery. In fact, neither Cruz nor any other conservative is trying to shut down the government. They intend to pass a continuing resolution (why not a freaking budget, though?) that funds everything but the implementation of Obamacare. In other words, the GOP House would pass a budget that permitted every single aspect of government activites to proceed as normal, except for something that a large majority of people hate: Obamacare.
It would be the Senate Democrats and/or the Democrat President who would actually shut down the government by refusing to pass that resolution, in one case, or by vetoing it, in the second.
But the yeomen DNC propaganda hacks at WaPo will never report this truth so baldly. In fact, as just demonstrated, they much prefer simply to lie about it.