Washington (CNN) - He was a leading member of a bipartisan "Gang of Eight" Senators who pushed a comprehensive immigration reform bill through the chamber earlier this year.
But with that measure facing little hope of passage in the Republican-controlled House, Sen. Marco Rubio feels Congress should play small ball when it comes to approving any bills on immigration reform.
Alex Conant, spokesman for the first-term Republican from Florida, said Monday those who favor the comprehensive immigration overhaul passed by the Senate in June need to be "realistic in our expectations" of what the House might embrace.
"An all-or-nothing strategy on immigration reform would result in nothing. What is keeping us from progress on a series of immigration issues on which there is strong consensus is the fear that a conference committee on a limited bill will be used to negotiate a comprehensive one. We should take that option off the table so that we can begin to move on the things we agree on," Conant added in a statement to reporters.
He made similar comments to Breitbart.com over the weekend after Rubio on outlined an such an approach, which is favored by House Republican leaders.
"I still want to solve immigration. I think it's an important issue for the country to deal with. But I don't think that we should not do anything because we can't do everything. That was my original position and continues to be my preferred option because I just think we're going to get a better result that way," Rubio said Friday in an interview on CNN's "New Day."
"I think when you try to do anything big in Washington, it ends up running into headwinds. Now that's the direction the Senate went. I wanted to influence that process so I got involved in it. But I continue to believe that a series of sequential individual bills is the best way, the ideal way, to reform our immigration system," added Rubio in an interview with CNN anchor Kate Bolduan.
At the beginning of the year, Rubio advocated that Congress pass four or five separate bills on immigration reform. But he later became the most high profile member of the "Gang of Eight," which authored a bill that included an eventual pathway to citizenship for most undocumented immigrants.
Although Rubio, who's Cuban-American, made numerous appearances on conservative talk radio in support of the measure, many on the right still oppose the Senate legislation. And Rubio, who is considered a potential candidate for the 2016 GOP presidential nomination, may have hurt his standing with conservative voters.
Once considered a rock star among many tea party activists and other grassroots conservatives, Rubio saw his poll numbers drop in a couple of hypothetical GOP nomination polls of Republican voters.
Rubio dramatically cut back the time he spent speaking about the issue of immigration reform following Senate passage. Instead, he highlighted his opposition to the health care law, in what appeared to be an attempt to repair his standing on the right.
He made no references to the immigration bill at the social conservative Value Voters summit earlier this month.
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