The full Senate will begin considering the legislation, which passed the Judiciary Committee last month on a 13-5 vote, next week.

Rubio, considered critical to the success or failure of immigration reform, is mulling a measure that would put Congress – rather than the Department of Homeland Security — in charge of drafting the border control strategy that is tied to the pathway to citizenship for undocumented immigrants in the United States.

“We don’t want to be back here in two years, in five years, 10 years dealing with another 5 or 10 million illegal immigrants,” Rubio said. “And so that’s the key. And people don’t trust the Department of Homeland Security to do this job or to come up with a plan that will do the job.”