Rubio: Majority of GOP Support Immigration Reform

A vast majority of Republicans and conservatives support immigration reform if the law solves the problem of illegal immigration for good, Sen. Marco Rubio, R-Fla., told CNBC on Tuesday.

As the most high-profile conservative in the bipartisan "Gang of Eight" senators who crafted the bill, Rubio said in a "Squawk Box" interview the bill that passed the Senate Judiciary Committee last month is a good "starting point."

"Our goal here is to pass a law, not just a bill," he explained—saying he would expect President Barack Obama to ultimately sign legislation approved by lawmakers.

The full Senate is expected to begin debate last this month on the "Gang of Eight" bill that includes putting 11 million illegal residents on a 13-year pathway to citizenship, provided they pay back taxes and a fine, learn English, hold a job, and pass criminal background checks.

Rubio said conservatives are split on the path to citizenship, but stressed that "we need to deal with people who are here now illegally because they're not going anywhere."

"Most, if they go through this process," he continued, "pay the consequences for violating our laws, then we should give them a chance to become Americans."

The measure also calls for tighter border control, but Rubio said those aspects need further improvement to win over lawmakers who "don't trust just turning it over to the Department of Homeland Security to come up with a plan."

As for the provision to create a national electronic worker verification system, known as E-Verify, Rubio said, "we need to ensure that we make it harder for people to find jobs if they're here illegally in the future to take away that magnate."

As a Cuban-American, Rubio is uniquely qualified to garner GOP support in the Democrat-controlled Senate, but also to help convince harder line conservatives in the Republican-controlled House.

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.