Perry signed the original Texas "DREAM" Act into law in 2001, and defended it as a compassionate move when it came under scrutiny during his 2012 run for president.

"If you say that we should not educate children who come into our state for no other reason than that they've been brought their through no fault of their own, I don't think you have a heart," Perry said at the time, during a 2011 GOP primary debate.

"We need to be educating these children because they will become a drag on our society...Texas voted on it. And I still support it today."

But on Monday, a Texas Senate committee will take up a bill rolling back the law. It's expected to pass in the Senate, but could face a tougher time passing the Texas House.

The original bill provides in-state tuition benefits for non-citizens who lived in the state for at least three years before graduating high school, and requires those receiving benefits to indicate they plan to apply for citizenship as soon as possible.

Perry made his efforts to secure Texas' border a central aspect of his pitch to Republicans in 2012 and is likely to do so again if he launches a presidential bid this cycle, as is expected. But he's made some more moderate comments on illegal immigrants, including his support for the Texas DREAM Act, that could put him in hot water with conservatives who want to see stricter controls on illegal immigration and enforcement of the country's immigration laws.

And this time around, he may take a more cautious approach on the law. Perry spokeswoman Lucy Nashed defended the law in economic, rather than emotional terms in an email to CNN.

"This was an economic decision that Texas was forced to make because of the federal government's failure to secure the border," she said. "This decision allows these young people to become productive, contributing members of society."