When the U.S. Supreme Court hears arguments Monday in the nation's most closely watched immigration lawsuit, Libia Rodriguez will be among the expected thousands of demonstrators at the court's white marble steps.

The case, United States v. Texas, could be a life-changer for Rodriguez, 31, an undocumented Mexican immigrant who lives in Coatesville with her husband, also here illegally, and their three U.S.-born children. Depending on the justices' ruling, the couple could put aside their worries of being sent back to Mexico. Or they could go on as they have for 13 years, uncertain of their family's future.

At issue are a pair of 2014 executive actions by President Obama, in response to congressional inaction on immigration reform. One would give limited protection from deportation to undocumented immigrants whose children are American citizens or permanent legal residents. The other would increase the number of undocumented youths, initially one million, who were protected under a 2012 executive action.

Between the Deferred Action for Parents of Americans (DAPA) and the Deferred Action for Childhood Arrivals (DACA) plans, 4.9 million of the nation's 11.3 million undocumented immigrants would be shielded from deportation.

Both executive actions, however, were swiftly blocked. Twenty-six states (not including Pennsylvania or New Jersey) sued, arguing that Obama had exceeded his authority. In February 2015, a federal judge in Texas issued an injunction, which was upheld by a Fifth Circuit panel. The Department of Justice appealed, setting the stage for Monday's arguments before the high court. A ruling is expected by the end of June.

Rodriguez, a homemaker who hopes to one day get an outside job, and her husband, a cement contractor, would be covered by DAPA. They met during their trek across the Sonoran Desert, from which they entered Arizona illegally in 2003. Their children, having been born here, are U.S. citizens.

"I really need this," she said of DAPA, under which she'd be eligible for a work permit and driver's license. "Permission would change our lives."

Driver's licenses, among other services, are part of Texas' argument. The state, the lead plaintiff, contends that Obama's executive actions will cause harm by requiring Texas to spend millions of dollars to provide driver's licenses to the many immigrants who will be allowed to stay in this country.

More pointedly, the plaintiffs accuse Obama of exceeding his authority, usurping powers that they say belong to the legislature.

The federal government has responded that presidents for decades have issued executive actions on immigration and that Obama's are no different.

With immigration issues galvanizing the electorate this year, advocates for undocumented immigrants and supporters of mass deportations have a lot invested in the outcome.

Marshall Fitz, of the Center for American Progress, a left-leaning think tank in Washington, called the case "a political dispute dressed up as a lawsuit."

House Speaker Paul Ryan (R., Wis.) saw a power grab: "This executive amnesty is a direct attack on Congress' . . . powers under our Constitution."

More than 50 interest groups - including the AFL-CIO, the National Sheriffs' Association, the Mexican American Legal Defense and Educational Fund, the National Queer Asian Pacific Islander Alliance, and a group of former Homeland Security officials - have filed friend-of-the-court briefs.

Buses carrying local advocates for immigrants will leave very early Monday from York, Reading, and Philadelphia.

Veteran court watcher Lyle Denniston, in a SCOTUSblog posting last week, said the case reflected the partisan polarization of the nation. "It is a modern echo of what the Founders debated with great intensity," he wrote. "How to divide up the powers of national and state governments?"

Recognizing the intense interest, the high court has allotted 90 minutes to the arguments, instead of the usual hour. The Department of Justice will share 10 of its 45 minutes with a lawyer for undocumented parents. Texas will give 15 of its 45 to a lawyer for the House of Representatives.

The justices told the parties to prepare to answer four fundamental questions:

Do the states have standing to sue?

Is the executive action "arbitrary, capricious, or otherwise not in accordance with the law"?

Did Obama bypass the "notice-and-comment procedures" in the Administrative Procedures Act?

Did he violate the Constitution's "take care" clause, to "faithfully execute" laws as passed by Congress?

The federal government is expected to argue that Obama acted pragmatically, prioritizing some deportations and deferring others because Congress appropriates only enough funding to remove 400,000 undocumented immigrants a year.

Attorneys for Texas are expected to argue that Obama's actions "grant lawful presence to aliens who would otherwise be unlawfully present."

No one is sure how the court will align. Some observers say Justices John G. Roberts Jr. and Anthony M. Kennedy are the likely swing votes.

The death of Justice Antonin Scalia in February creates the possibility of a 4-4 ruling. A tie would leave in place the lower court's injunction.

If the justices uphold the 2014 actions, the Obama administration would be left with just a few months to begin carrying them out. Democratic candidates Hillary Clinton and Bernie Sanders have said they would continue them, while the leading Republican candidates have promised to put the Obama actions on the chopping block in 2017.

Drexel University associate professor of law Anil Kalhan wrote about United States v. Texas for the UCLA Law Review. He criticized the District Court for basing its injunction on "the same incorrect claims about deferred action" heard in populist anti-immigration rhetoric.

"One of the big-picture things I've been struck by," Kalhan said in an interview, "is the way the norms of political discourse, which are really toxic, charged and divisive, are bleeding into the litigation process. . . . The Supreme Court has an opportunity to draw a line."

mmatza@phillynews.com

215-854-2541@MichaelMatza1