The justices said they will consider undoing lower court orders that blocked the plan from taking effect in the midst of a presidential campaign that already roiled by the issue.
The case will be argued in April and decided by late June, about a month before both parties' gather for their nominating conventions.
The immigrants who would benefit from the administration's plan are mainly the parents of US citizens and lawful permanent residents.
So far, the federal courts have sided with the states to keep the administration from issuing work permits and allowing the immigrants to begin receiving some federal benefits.
If the justices eventually side with the administration, that would leave roughly seven months in Obama's presidency to implement his plans.
At issue is the Deferred Action for Parents of Americans program, which Obama said in late 2014 would allow people who have been in the United States more than five years and who have children who are in the country legally to "come out of the shadows and get right with the law."
Solicitor General Donald Verrilli Jr said in his court filing that allowing those rulings to stand would force millions of people "to continue to work off the books, without the option of lawful employment to provide for their families."
The administration said Texas and the other states don't even have the right to challenge the plan in federal court.
The future of the estimated 11 million immigrants living in the country illegally has been much discussed by Republican and Democratic presidential candidates. Democratic front-runner Hillary Rodham Clinton has pledged to go further than Obama to protect large groups of immigrants from deportation.
Obama said he was spurred to act on his own by Congress' failure to pass comprehensive immigration legislation. An earlier program that is not being challenged, Deferred Action for Childhood Arrivals, shields immigrants brought to the country illegally as children.
