The plan would lift the threat of deportation from 5 million migrants living illegally in the US.
A coalition of 26 mostly conservative states, led by Texas, has been successful in lower court challenges.
A decision from the Supreme Court is expected in the early summer, just as the election gets into full swing.
“We are confident that the policies will be upheld as lawful,” said White House spokeswoman Brandi Hoffine.
President Barack Obama announced the plan, known as Deferred Action for Parents of Americans and Lawful Permanent Residents (DAPA), in November 2014.
He justified using his presidential powers, without Congress, by saying it was in response to inaction over the issue of immigration from Congress.
If allowed to go forward, it would allow people who have lived in the US for more than five years and who have children who are living in the country legally to apply for work authorization.
In announcing the plan, Barack Obama said it would allow those who qualify to “come out of the shadows and get right with the law”.
Challenges to the plan began shortly after President Barack Obama’s announcement, with a federal court in Texas effectively putting a pause on it in February.
The Obama administration lost an appeal in November, keeping the injunction in place.
The White House has vowed to kickstart the program if the Supreme Court was to rule in its favor, so that migrants could began enrolling before a new president takes office in January 2017.
One of the largest questions looming over the case is whether the state challengers have the right to do so.
Texas argues it will have to spend millions of dollars to provide driver’s licenses to people who are part of the program.
The issue of immigration has become a controversial and polarizing issue in the 2016 presidential race.
Leading Democrat presidential candidate Hillary Clinton has said she would maintain and expand President Barack Obama’s reforms, while Republican front runner Donald Trump has said he would reverse the reforms and step up enforcement.
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