By JOSH GERSTEIN | 12/12/11 10:33 AM EST Updated: 12/12/11 11:56 AM EST

The Supreme Court on Monday agreed to consider whether a law Arizona passed last year cracking down on illegal immigration violates the Constitution by intruding on the prerogatives of the federal government.

The new high-profile platform for the continuing legal fight over immigration-related state laws has the potential to inflame the issue in the 2012 presidential campaign — a development that could benefit President Barack Obama’s appeal among Latinos, but hurt his standing with swing voters who are broadly supportive of legislation to rein in illegal immigration.

The Obama administration, which persuaded lower courts to block key parts of the Arizona law, known as S.B. 1070, had asked the Supreme Court not to take up the case at this time. Still, White House press secretary Jay Carney told reporters Monday, “You know the president’s position and the administration’s position. We look forward to arguing it in this case.”

The state of Arizona, which was on the losing end of the lower-court rulings, petitioned the justices to step in.

The Arizona law requires local police to try to determine the immigration status of people they detain during a traffic stop, arrest or questioning. It also appears to authorize police to hold individuals pending the outcome of an immigration check, though there has been some disagreement about the interpretation of that provision. The law also demands that foreigners have immigration papers in their possession at all times.

The fight over the Arizona immigration law is just one of several politically sensitive cases the high court is set to wrestle with in the upcoming presidential election year, including the health care law passed last year and a battle over redistricting of congressional seats in Texas. The same conservative attorney is lead counsel in all three cases: Bush administration solicitor general Paul Clement.

“With this morning’s decision to review the Arizona S.B. 1070 immigration case, there is no question that the Supreme Court’s 2012 Term will be a blockbuster,” said Elizabeth Wydra of the liberal Constitutional Accountability Center. “The constitutional challenge to the Affordable Care Act is already on the Court’s docket, and a challenge to Texas’s affirmative action policies is waiting in the wings — add to that a major immigration decision that implicates the federal-state balance of power, and you’ve got one of the most momentous Terms in recent Court history.”

Several other states have followed Arizona’s lead and enacted similar immigration-related legislation — to a greater or lesser degree. In recent months, the Justice Department has hit three of those states — Georgia, South Carolina and Utah — with lawsuits claiming their laws usurp federal authority.

The Supreme Court indicated that it was accepting the Arizona case via a set of orders released on the Internet Monday morning about a half-hour before the customary 10 A.M. release time, apparently due to a Web glitch.

Justice Elena Kagan, who was serving as solicitor general when the Arizona law was being challenged in the lower courts, did not take part in the decision to take the case. Such a statement generally means that the justice involved will also abstain from ruling on the merits of the issue when it is decided by the court.

In May, the Supreme Court, by a 5-3 vote, upheld another immigration-related Arizona law that threatened to revoke the business licenses of employers who repeatedly hired illegal immigrants. The Obama administration argued against that law, which was signed by Secretary of Homeland Security Janet Napolitano when she was governor of Arizona in 2007.