Cruz, who some surmise could be eyeing a presidential run in 2016, called out Vice President Joe Biden for his commitment to bring gun control legislation back to the Senate.
"If he believes the answer to violent crime is not prosecuting felons and fugitives, not prosecuting gun crimes but going after the constitutional rights of law-abiding citizens, I would like to invite the vice president to engage in an hour-long conversation and debate," Cruz said.
Former Alaska Gov. Sarah Palin also spoke to the crowd, telling the thousands gathered, "This is a fight for the future of freedom," and accusing the White House of playing politics with the families from Newtown and other shootings.
"This president [is] flying in grieving parents on Air Force One, making them perpetual backdrops," Palin said.
Some grieving families also came to the NRA convention, telling reporters just across the street from the convention center that they were there to try and reason with NRA members not take away Second Amendment rights.
"Everybody down deep knows what happened in Newtown was something that shouldn't have happened," said Neil Heslin, whose 6-year-old son Jesse Lewis was killed in the Sandy Hook school shooting, "and I think that anybody that's any sort of a human agrees that we should do whatever we could do to prevent ... tragedies like these from happening again.
"You're never going to stop all of it," Heslin added. "I lost my son. I never really gave much thought about it ever happening to me. I thought it couldn't happen to me. ... It could happen anywhere. It could happen here. It could happen in your hometown. It could happen to you. It could happen to anybody."
Also in Houston was Patricia Maisch, who helped wrestle a fresh magazine of bullets away from Jared Loughner as he tried to reload at the Tucson, Ariz., shooting in January 2011 that killed six and seriously injured others, including former Rep. Gabrielle Giffords. When the Manchin-Toomey amendment failed in the Senate, Maisch let her voice be heard, yelling, "Shame on you!" to the senators from a balcony.
"I went from being sad as I looked over the balcony and saw the senators going on with their lives, shaking hands, chatting -- and it just made me go from sad to mad, and I just decided I had to say something," Maisch said.
"They needed to be shamed," she added. "As far as I'm concerned, the NRA, the gun manufacturers, the gun lobby are saturated in blood, and some of our legislators have blood on their hands."
She said she and others like Heslin are "not just going to go away. We're here to stay."
"I don't know what we can do to convince them that we can have reasonable background checks and still preserve their Second Amendment rights," Maisch said, referring to the NRA leadership. "I don't believe that's what they are interested in. They are just interested in making money."
As for senators like Ayotte and Arizona Sen. Jeff Flake, who are hearing from angry constituents about their no votes, Maisch said she believes "they lost their souls that day."
In the convention hall, members walked around looking at the hundreds of gun exhibits displaying new weaponry and accessories.
Larry Miller and his wife, Philisha, came from nearby Shepherd, Texas, to support "the NRA and activism."
He told ABC News on the exhibition floor he is against universal background checks because there are already "thousands" of gun laws that are not being enforced.
"The one thing common in any homicide is a person," Miller said, "regardless of the inanimate object used. So why do we need more laws when we don't enforce the ones we already have?"
Philisha Miller said she believes "now more than ever, the NRA needs as much support as possible."
"As far as the state of the NRA, I believe they are stronger than ever," Miller said.
Other big-name Republicans at the event included Louisiana Gov. Bobby Jindal and former Sen. Rick Santorum of Pennsylvania.
It was the first of the NRA's annual meetings with Birmingham, Ala., attorney, Jim Porter, as president of the organization.
ABC News' Jeff Zeleny contributed to this report.