Rubio: Immigration deal 'un-doable' if health benefits are on the table

"ObamaCare is the only federal benefit where you qualify for it not because you have a green card but because you're lawfully present. That issue needs to be resolved," he said.

Rubio is one of eight senators who unveiled principles for immigration reform on Monday. That bipartisan framework allows undocumented immigrants to earn a probationary legal status, but not public benefits through the Affordable Care Act's insurance exchanges or its Medicaid expansion.

Rubio spoke with several conservative outlets Tuesday to pitch the Senate framework to the Republican base.

President Obama released his own proposal Tuesday, which would make it somewhat easier for people without papers to gain citizenship than under the Senate proposal.

A fact sheet released by the White House said Obama's plan would not allow provisionally legal immigrants access to federal benefits, including assistance under the Affordable Care Act.

Current law allows almost anyone with a legal status access to those benefits.

—This post was updated at 5:54 p.m.