Then, with the country facing a debt default, leaders in the Democratic-led Senate brokered a deal to end the standoff — which Cruz dismissed as "selling the American people down the river."
"You don't win a fight when your own team is firing cannons at the people who are standing up and leading, which are the House Republicans," he said. "That's what happened, and that's what led directly to this lousy deal, is when Senate Republicans declined to unify and declined to support House Republicans."
The deal sets up the potential for another budget showdown in January. Senate GOP leaders, however, have suggested that there won't be a repeat of the shutdown or a potential default crisis like in recent weeks.
But addressing reporters after his speech, Cruz would not say that another fight won't be coming.
"There will be plenty of time to consider the particular practical or strategic decisions," he said.
Asked if he was worried about retaliation from more-senior Republican leaders in the Senate, Cruz said, "I try very hard not to worry about the politics and the internal back-and-forth in Washington."
"My focus is on doing my job," he said.
Saturday's crowd was mostly sympathetic, with many convention attendees giving Cruz a standing ovation at the end of his speech. Some stayed seated, though.
"Obamacare isn't working, and not only is it not working, it's not working badly," Cruz said.
He said because the nation's new health care law has price limits that restrict discrepancies between what young Americans buying insurance pay and what older customers pay, it was a "massive wealth transfer" from healthy young people "who are struggling, just starting their career, to everybody else."
Cruz said the rollout of online health care exchanges where customers can buy insurance coverage has been full of glitches — but he said that those would be resolved, while fundamental flaws in the law will endure.
"They'll get the technical things worked out," he said. "Eventually they'll hire a programmer who can find his rear end with both hands."
Many political observers now see Cruz as Texas' most popular Republican. His approval ratings across the country may be slipping a bit, however.
National polls have shown that while Americans in general don't love the health care law, they oppose defunding it — especially if it means shutting down the government. Many of Cruz's Senate colleagues, meanwhile, have bemoaned the shutdown for tarnishing the GOP's image nationally.
Cruz also took questions from the audience and was asked if ideology driving Washington could outweigh political pragmatism.
"The arguments I have laid out today have not been ideological," Cruz said. "These were the essence of practical."