Washington (CNN) - Sen. Marco Rubio, the most prominent Republican working towards immigration reform, continued to argue Tuesday he's not pursuing the issue for his own political agenda and weighed in on his thoughts about 2016.
Applauding the Senate's decision to move forward with a border security amendment Monday night, the first-term senator also acknowledged the difficult position he's been in as he faces criticism from his own party.
"This amendment basically now puts into place virtually everything people have been asking me to do about immigration enforcement since I began talking about this issue," Rubio said during a speech to the American Society of News Editors in Washington.
He ticked off a number of the provisions in the compromise amendment, which includes 20,000 more border agents, the completion of 700 miles of fence along the boundary with Mexico, and $3.2 billion in technology upgrades, among other items.
The Senate decided to proceed with the amendment Monday in a 67-to-27 vote that helped clear a major hurdle for the comprehensive package drafted by the bipartisan group of senators known as the Gang of Eight.
The senator from Florida said the politics of immigration reform is "overrated," reiterating his full-throated defense that he's seeking immigration changes out of concern for the country, rather than concern for his political future. "Quite frankly, the politics of it are probably not that positive, certainly in the short term."
Widely considered a potential 2016 presidential contender, Rubio said Tuesday he "really (doesn't) think about that right now," arguing he first has to decide next year whether he'll run for re-election in the Senate before he considers a path to the White House.
"I also want to make sure I have something to contribute. I don't want to just hold office, whether it's in the Senate for re-election or for president or something else, simply because I can," he said. "I'm not at that stage yet."
Rubio, who was elected in 2010 with strong tea party support, also said thinking about higher office "begins to influence the way you behave politically-the decisions you make, the issues you take on, the stances that you adopt," adding he wants to stay focused on his current job.
While some Republicans have been heralding immigration reform as a chance to win more votes in the rising Hispanic community, Rubio said he has never presented it from that angle but acknowledged the voting demographic could look different down the road if immigration reform becomes law.
"I would not look at how people feel today politically and say that's how they're going to feel 10-15 years from now," he said. "America changes immigrants…People will change, especially once they begin to become fully enveloped in the American economic experience."
The Senate could start voting on the full package this week. If it passes, it then heads to the Republican-controlled House of Representatives, where House Speaker John Boehner has stated he won't take up the bill unless it has support from a majority of House Republicans.
Asked what he thinks will happen in the chamber, Rubio said the House is "going to do what the House wants to do" and made the case that the body should consider the Senate version of the bill.
"But ultimately they're going to have their own process and I'm not going to tell them how to run it," he said, predicting the House version will "look substantially different" from the Senate bill, especially on border security and the timeline for legal status of undocumented immigrants.
The biggest challenge that lies ahead, he added, is winning confidence from the public that the government can actually carry out the border security provisions the bill employs. Citing low approval ratings for Congress and a series of controversies plaguing the Obama administration, Rubio said "trust in the federal government today is probably as low as it's been since Watergate."
Growing more impassioned in his speech, Rubio devoted a substantial amount of time to talking about the country's history of immigration and his own family's story of emigrating from Cuba.
"Somehow all these different people from all these different places created the single greatest nation man has ever known, and I refuse to believe that we're still not that country," he said. "Because if we are, then we've lost the essence of who we are and the world has lost its greatest hope-that shining city on the hill."
– CNN's Alan Silverleib and Dana Bash contributed to this report.