WASHINGTON — Immigration politics will hit the Supreme Court this week as justices consider how much border-control clout the states can deploy.

The court must decide whether Arizona went too far with a crackdown that includes ordering police to routinely check the legal residency status of people they stop. The court’s ruling answer this election year could ignite Capitol Hill, other states and, especially, Hispanic voters.

“This is a huge case, of great importance,” said Andrew I. Schoenholtz, a visiting professor of law at the Georgetown University Law Center.

Arizona v. United States, the case being heard Wednesday, carries well beyond the notoriously porous Southwest border. South Carolina, Idaho, Florida and 13 other states have allied themselves with Arizona, arguing for the power to impose certain immigration measures if they choose. House Minority Leader Nancy Pelosi and 16 other House Democrats from California take the opposite position. On both sides, dozens of friend-of-the-court briefs press different points.

The court’s decision is likely to come in June, as the campaign season is heating up and about the same time as the court is expected to rule on the Obama administration’s signature health care law. While a decision to uphold the strict Arizona law would be a legal defeat for the Obama administration, some scholars predict it could help the president politically by boosting turnout among the nation’s 21 million voting-age Hispanics.

“Fear is a remarkable mobilizer,” said Gary Segura, a Stanford University pollster and political science professor.

Citing failures by Congress to deal effectively with immigration and the estimated 11 illegal immigrants living in the United States, Arizona legislators included several far-reaching provisions in the 2010 law. The most controversial, and the one that may cause the court the most difficulty, deals with checking U.S. residency status.

Under the Arizona law, police who detain people for other reasons must check their residency status if the officers have a “reasonable suspicion” that they are illegal immigrants. When someone is arrested, residency status must be confirmed before the person is released.

The law also makes it a state crime to be in the United States without authorization, as well as a state crime for an illegal immigrant to work or seek work without authorization.

“Arizona and its 370-mile border are a conduit for rampant illegal entries and cross-border smuggling,” Arizona’s attorney, Paul Clement, wrote in a brief. “The public safety and economic strains that this places on Arizona and its residents have created an emergency situation, which demanded a response.”

Trial judges have blocked the Arizona law from taking effect, reasoning that states can’t trample on the federal government’s border control responsibilities. The Supreme Court will determine whether state action is pre-empted by the various immigration laws passed by Congress.

The federal government thinks so.

“It is the national government that has ultimate responsibility to regulate the treatment of aliens while on American soil, because it is the nation as a whole, not any single state, that must respond to the international consequences of such treatment,” Solicitor General Donald Verrilli Jr. wrote.

Verrilli further argued that Arizona’s law is an “attempt to hijack” federal enforcement responsibilities, while Clement soothingly characterizes the state’s effort as one of collaborating with federal counterparts.

The Supreme Court, in a 5-3 decision last year, upheld a separate Arizona provision that suspends or revokes the business licenses of employers that knowingly hire illegal immigrants.

Some states and localities, in particular, have become very aggressive. Alabama legislators last year passed a law that bans illegal immigrants from attending the state’s public colleges and universities, requires elementary schools to check their students’ residency status and bans illegal immigrants from renting property, among other provisions.

Justice Elena Kagan will not participate as her former solicitor general’s office colleagues tried to block Arizona’s law. If the eight remaining justices are deadlocked, the 9th I.S. Circuit Court of Appeals decision striking down the Arizona provisions would preval, although no national precedent would be set.

The hourlong oral argument in the Arizona immigration case is the last one scheduled for the Supreme Court term that began last October. Justices usually deliver their final opinions in the last week of June.