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

In their latest highly charged faceoff, the justices 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 final answer this election year could ignite Capitol Hill, other states and, not least, 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.

Called 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 tack. On both sides, dozens of amicus briefs press different points.

The court’s final decision, moreover, 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,” Stanford University pollster and political science professor Gary Segura said, “is a remarkable mobilizer.”

Citing congressional failures to deal effectively with immigration, as well as the estimated 11 million illegal immigrants now 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 greatest difficulty, deals with checking U.S. residency status.

The state law requires that Arizona law enforcement personnel who have detained individuals for other reasons check their residency status if the officers have a “reasonable suspicion” that they’re illegal immigrants. When someone is arrested, residency status must be confirmed before the person is released.

The Arizona Support Our Law Enforcement and Safe Neighborhoods Act 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.”

Clement also is representing Florida and other states in the separate case challenging the health care law.

Trial judges have blocked the Arizona law provisions from taking effect, reasoning that states can’t trample on the federal government’s border control responsibilities. The high court will be determining whether state action is preempted 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 already has voiced some sympathy for states that enact immigration crackdowns amid congressional gridlock. Last year, in a 5-3 decision, the court upheld a separate Arizona provision that suspends or revokes the business licenses of employers that knowingly hire illegal immigrants.

“Perhaps Congress never expected that the states would have to resort to such massive measures, and they probably wouldn’t have if the law had been uniformly enforced and vigorously enforced, right?” Justice Antonin Scalia retorted during the earlier oral argument.

Some states and localities, in particular, have become very aggressive. Alabama legislators, notably, passed a law last year 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 try to block Arizona’s law. If the eight remaining justices tie 4-4, the 9th Circuit Court of Appeals decision striking down the Arizona provisions will be upheld, though without setting national precedent.

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