(CBS News) WASHINGTON - Police and politicians are trying to come to grips with theon Arizona's controversial, tough immigration law.
The justices struck down most of it, but ruled unanimously that police in Arizona are still allowed to check any suspect's immigration status.
However, in a five-to-three vote, the court struck down three other parts of the law.
One requires immigrants to carry registration papers wherever they go.
Another makes it illegal for undocumented residents to seek work or hold a job in Arizona.
And another allows police to arrest suspected illegal immigrants without a warrant.
The overall ruling didn't really make anybody happy, as Democrats and Republicans each scrambled to spin the court's words in their favor after what was certainly a mixed opinion.
The court unanimously agreed to uphold the most controversial section of Arizona's immigration, law known as "show me your papers," which requires police to check the immigration status of people they've stopped for another violation.
CBS News political director John Dickerson offered analysis of the decision's possible impact on the presidential race spoke to "CBS This Morning" co-hosts Charlie Rose and Erica Hill. To see that discussion, click on the video below:
For the Obama administration, which opposes the law, it was at least a partial victory.
The court threw down some limits on Arizona, striking down parts of the law that created new state crimes for immigration violations, ruling that immigration enforcement was the federal government's job.
That left the two presidential candidates, who have very different views on immigration, praising and criticizing completely different parts of the decision.
President Obama said in a statement he was "pleased that the Supreme Court has struck down key provisions of Arizona's immigration law." But he didn't stop there, adding he is "concerned about the practical impact of the remaining provision" requiring immigration background checks.
Presumptive Republican nominee Mitt Romney, who was in Arizona Monday, said at a fundraiser that he "would have preferred to see the Supreme Court give more latitude to the states, not less."
Romney has said immigration would be a priority for his first year in office. But he has not gone into specifics about what he would do, as he tries to appeal to Latino voters without alienating conservatives.
That balancing act led to a contentious exchange between Romney spokesperson Rick Gorka and reporters asking for more details.
Asked if Romney agrees with the Supreme Court or Arizona, Gorka replied, "Our position is clear on this."
"It's not," a reporter contended.
"It is," Gorka insisted. "The president has failed to address illegal immigration."
Republican Sen. Marco Rubio, of Florida, himself the son of Cuban immigrants, told Charlie Rose on Rose's show on PBS that the decision underscored the need for federal immigration reform.
"I think they have a constitutional right to pass a law like this," Rubio said. "I understand why they passed a law like this. But I don't think it's a national model."
The Obama campaign believes that, politically, at least, this law wasn't so bad. The administration is going to continue to fight it. Mr. Obama suggested Monday that the provision the high court left in place could lead to racial profiling.
All of that, of course, could help rally Hispanics, which could be decisive in November.
To see Jan Crawford's report, click on the video in the player above.