Vargas outed himself last year as one of the nearly 12 million undocumented workers in the United States. A Pulitzer Prize winner, he wrote the Time cover story, saying there hasn't been an honest discussion in the U.S. about the issue.
"We are not who you think we are," Vargas said Thursday on "CBS This Morning." "To me, the power of this Time magazine cover is, you have 35 people here from 15 different countries, Mexico, Nigeria, Israel, Korea, Philippines. You know, when we think about illegal immigration, we seem think it's all about Mexicans and the border. That's not the reality."
In the political world, Vargas said this has become "a third rail issue." "Politicians don't want to touch this," he said. "Because, again, I don't think we've had an honest conversation about it. It's really tough to talk about any pieces of legislation without first having an honest conversation about what we're talking about."
Vargas lives under the threat of deportation. "All 35 of us on this cover worry about it," he said. "But what's even more worrisome is not doing anything about it."
Vargas said there's currently not a process in place for illegal immigrants to become residents of the United States.
"I remember being in Iowa in Cedar Rapids and Mitt Romney telling the audience (that) people like me should get in the back of the line," He said. "Where is the line? If they can tell us where it is, if it's in Times Square somewhere, I'll go there right now. There is no line, there is no process."
Since he came out as an undocumented worker, Vargas said he has not been approached by the government. In fact, he said even called a government agency and was told he was not in their database and that they couldn't talk about his case with him.
"At the end of the day, most people in my situation haven't been encountered by the government. There's 11.5 million of us, right? Most people have not been encountered," he said. "... I am about as public as it comes on this. I'm on Twitter, I'm on Facebook. I'm on the corner of 14th and 6th in Manhattan."
Vargas said the debate going forward "should be an actual solution. The debate should be an actual compromise. The debate should be about an honest conversation about this issue."
Vargas suggested that a system that gives people the chance to come forward would be fair. "We're almost invisibly visible," he said. "You know we're here. So allow us to come forward and say, 'Hey, if you want us to pay our back taxes, if you want us to wait in some sort of line. If you want us to learn to speak English,' ... But give us the process that we can enter."
When asked if that's inequitable to people that have entered the country legally, Vargas replied, "The thing to me is, what's more counterproductive is allowing people like me to even stay in the shadows. For example...people didn't know that we pay taxes. In 2010, we paid $11.2 billion in state and local taxes. We pay into Social Security, yet we can't benefit." Vargas said he is paid as an independent contractor.
For more with Vargas, watch his full "CTM" interview in the video in the player above.