Attorney general nominee Sen. Jeff Sessions, R-Ala., signaled support on Tuesday for repealing President Obama's executive action allowing hundreds of thousands of children of illegal immigrants to remain in the United States without fear of deportation.

Specifically on whether Sessions would try to persuade President-elect Trump to overturn the executive action known as the Deferred Action for Childhood Arrivals, or DACA, Sessions suggested that the move might have been unconstitutional, but said a study is first needed about the impact of rescinding it.

The Alabama Republican said DACA is "very questionable, in my opinion, constitutionally" so he doesn't believe the Department of Justice would object to repealing it. "It would certainly be constitutional, I believe, to end that order," he said.

Sessions was responding to questions from Sen. Lindsey Graham, R-S.C., on whether he would advise Trump to repeal DACA. The program allows children of illegal immigrants who are under the age of 31 and have been in the country before age 16 to remain without fear of deportation.

Sessions has opposed DACA, and on the campaign trail, Trump was a critic of the program but more recently has suggested he is open to a compromise on the issue.

"Fundamentally, we need to fix this immigration system," Sessions said when asked by Graham what should be done with the nearly 800,000 people who have been protected from deportation under DACA.

Sen. Dick Durbin, D-Ill., also pressed Sessions on the issue, noted that it's easy for Sessions to ask Congress to write an immigration law after opposing all of the bipartisan compromise the Senate has produced in "modern memory."

When asked what the Trump administration would do to people discovered to be living in the country illegally, Sessions suggested that current law and limited federal finances would prevent mass deportations, although Trump, like Obama, would likely put a priority on deporting criminals and terrorists.

"As you know, Sen. Dick Durbin, we're not able financially or any other way, to seek and remove everyone in the country illegally," he said.