Arizona's Republican Senators, John McCain and Jon Kyl, said in a joint statement that they would "fully review" the ruling but vowed to keep fighting "to secure our southern border" and accused Obama of enforcing immigration rules "based on a political agenda, not the laws as written by Congress."
"We believe Arizonans are better served when state and federal officials work as partners to protect our citizens rather than as litigants in a courtroom," the senators said.
"I will work with anyone in Congress who's willing to make progress on comprehensive immigration reform that addresses our economic needs and security needs, and upholds our tradition as a nation of laws and a nation of immigrants," Obama said. "And in the meantime, we will continue to use every federal resource to protect the safety and civil rights of all Americans, and treat all our people with dignity and respect."
Romney has struggled with immigration on the campaign trail: He said he would veto the DREAM Act if it passed when he was president. In a speech last week to Latino officials, he said he would offer a long-term solution that would "replace and supersede" Obama's decision to halt deportations of some 800,000 young undocumented immigrants brought to U.S. soil as children. But details of his plan remained vague.
The Republican base is fiercely anti-undocumented immigration. The Obama Administration has carried out a record number of deportations -- but conservatives accuse him of lax enforcement of the country's immigration laws.
Rick Santorum, who challenged Romney from the right, said in a statement on the court's ruling that "it's time for the federal government to step up to its constitutional responsibility to secure our borders, enforce our immigration laws fairly, and to partner with states rather than sue them to accomplish this important objective."
And Arizona Governor Jan Brewer immediately applauded the court's ruling as "a victory for the rule of law" and a "loss" for opponents of her state's approach. Brewer said police engaged in racial profiling would be punished.
"I am confident our officers are prepared to carry out this law responsibly and lawfully. Nothing less is acceptable," she said, noting that foes of the measure are sure to challenge it in court again if it is enforced unfairly.
Democratic Senator Chuck Schumer said the Supreme Court had delivered "a stern warning" to Arizona regarding the implementation of that provision.
And "this decision tells us that states cannot take the law into their own hands," he said in a statement. "The only real solution to immigration reform is a compehensive federal law."