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Less than a month after hearing a challenge to the controversial Obama health care law brought by 26 states, the Supreme Court today will explore the relationship between the federal government and the states on another hot-button issue: immigration.

At issue is S.B. 1070 - Arizona's strict immigration law that empowers local police to enforce federal immigration laws. It was signed by Gov. Jan Brewer who says that the law was needed to combat illegal immigration.

"It costs us about 1.6 billion dollars a year in health care, incarceration and education," Brewer said. "It's out of control."

The arguments will mark a rematch between the Obama administration's top lawyer, Solicitor General Donald B. Verrilli Jr., and Paul Clement, who will argue on behalf of Arizona and who also represented the states in the challenge to the Affordable Care Act.

Almost immediately after S.B. 1070 passed in 2010, the Obama administration challenged the law. A lower court sided with the government and froze four controversial provisions from going into effect.

One of the provisions requires local law enforcement officers to request immigration papers from anyone they stop, if the officer has a "reasonable suspicion" that the individual is in the country illegally. Another criminalizes unauthorized work, and a third makes it a state crime to fail to carry immigration papers at all times. A fourth provision allows law enforcement to make an arrest without a warrant when an officer has probable cause to believe an individual has committed an offense that would result in a person's deportation.

The Obama administration argues that the Constitution gives the federal government authority over immigration and that the state law conflicts with existing federal law.

"As the Framers understood, 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," Verrilli wrote in court papers.

He argues that while the federal government welcomes the assistance of state officers, Arizona is trying to adopt its own immigration policy while paying no heed to the Immigration and Nationality Act (INA), the principal federal immigration statute that establishes a scheme for the regulation of immigration.

The law takes into consideration humanitarian conditions, foreign-policy considerations and other issues when deciding whether someone should be deported.  "Arizona has adopted its own immigration policy, which focuses solely on maximum enforcement and pays no heed to the multifaceted judgments that the INA provides for the Executive Branch to make," Verrilli wrote.

"For each state, and each locality, to set its own immigration policy in that fashion would wholly subvert Congress's goal: a single, national approach," he continued.

But Clement says in court papers that Arizona shoulders a disproportionate burden of the national illegal immigration problem, and that SB 1070 was passed to supplement the "the federal government's inadequate immigration enforcement."

"Arizona was acutely aware of the need to respect federal authority to set the substantive rules governing immigration, and carefully crafted a bill to respect Congress' policy determinations and definitions while enhancing the State's contribution to the enforcement efforts," Clement wrote.

Kris Kobach, a long time advocate of immigration reform, helped draft the law and others like it in other states.  Kobach, who currently serves as Kansas's secretary of state, believes the Supreme Court will reverse the lower court and uphold the provisions.

"The Supreme Court has said again and again that there is a role for the states to play," Kobach said. "Congress is the primary actor in the field, but the states are permitted to act too, as long as Congress doesn't ask them to get off the field."

Immigrants' rights advocates say the law will lead to racial profiling.  Wade Henderson, president and CEO of The Leadership Conference on Civil and Human Rights, issued a statement saying S.B. 1070 rewrites "the entire relationship between states and our federal government."

"These laws don't just target immigrants," Henderson said.  "American citizens, particularly people of color have, had their lives disrupted, been detained, and subject to needless ad hoc immigration trials by local law enforcement officials who are poorly equipped to interpret the complex federal web of federal immigration laws."

Justice Elena Kagan will not participate in the case, presumably because she dealt with the issue in her previous job as U.S. solicitor general. The Court is expected to release a decision near the end of June, most likely around the same time it decides the health care case.

ABC News' Steve Portnoy contributed to this report.