Marco RubioMarco Antonio RubioOvernight Cybersecurity: Bipartisan bill aims to deter election interference | Russian hackers target Senate | House Intel panel subpoenas Bannon | DHS giving 'active defense' cyber tools to private sector Senators unveil bipartisan push to deter future election interference Puerto Rico's children need recovery funds MORE on Sunday shot back against fellow Republican presidential hopeful Ted CruzRafael (Ted) Edward CruzWith religious liberty memo, Trump made America free to be faithful again Interstate compacts aren't the right way to fix occupational licensing laws Texas Dem: ‘I don’t know what to believe’ about what Trump wants for wall MORE, saying the Texas senator's campaign is built on a lie that he's the "only conservative and everyone else is a sellout."

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Cruz has said that both he and Rubio ran promising to block amnesty, but Rubio broke that promise. Rubio noted on CNN's "State of the Union," however, that Cruz helped design George W. Bush's immigration policy and talked openly about needing to reach a compromise on people that were in the country illegally.

"He said he wanted to bring people out of the shadows," Rubio said. "He said he wanted to obviously pass immigration reform so I think it's just not an accurate statement."

"It's a hard issue," Rubio added.

Rubio said he doesn't support amnesty.

"This whole notion Ted has that he's the only conservative, I think that as people learn more about his record, they'll realize that he's really very calculated," Rubio said.

Rubio also said Cruz is just "making stuff up," at this point.

"It's strange," he added.

Cruz has been taking at shots at Rubio, launching an ad in Iowa that calls Rubio the "Republican Obama."

Rubio said he will just continue to focus on his agenda and share his ideas.

Going into the Iowa caucuses on Monday, Rubio said does "feel good."

"We're gong to have a strong showing."