States seeking to take immigration enforcement into their own hands are facing an uphill climb, after the Supreme Court reined in Arizona's disputed law and the Obama administration followed by rescinding a key partnership allowing local police to enforce federal immigration rules.

The day's decisions further weakened efforts by Arizona, and potentially other states, to take on immigration enforcement themselves.

The high court decision Monday struck down three provisions in Arizona's law, including one that allowed local police to arrest anybody they suspect committed a deportable offense. The ruling left in place, though, a central plank that required local law enforcement during routine stops to check the immigration status of anyone they suspect is in the country illegally -- a provision Democrats claim could lead to "racial profiling," though Arizona Gov. Jan Brewer denies that.

The Obama administration quickly moved to deflate the remaining provision.

By Monday afternoon, the Department of Homeland Security had pulled back on a program known as 287(g), which allows the feds to deputize local officials to make immigration-based arrests. According to a Homeland Security official, the administration has determined those agreements are "not useful" now in states that have Arizona-style laws. Immigration and Customs Enforcement has since rescinded that agreement in Arizona -- with the state itself, and with three local law enforcement agencies.

The move means that even if local police step up immigration checks, they'll have to rely on federal officials to make the arrests.

And federal officials made clear that ICE would be selective in responding to the expected rise in calls from Arizona and other police agencies about immigration status. Officials said ICE will not respond to the scene unless the person in question meets certain criteria -- such as being wanted for a felony.

Brewer, in a statement released late Monday, excoriated the administration for the move. She said the decision showed Obama "has demonstrated anew his utter disregard for the safety and security of the Arizona people. ... We are on our own, apparently."

All these factors led some GOP officials to question the future of state-led efforts to tackle illegal immigration.

"We've lost the ability for states to take problems that they themselves are facing and do something about it," said Sen. Mike Lee, R-Utah, who represents one of several states that implemented their own Arizona-style laws.

Lee told Fox News that the Supreme Court decision means states "have to be careful not to run afoul" of the court's ruling. "It means it'll be more difficult for states to set their own penalties on conduct that's already against the law federally," he said. "The state governments have lost something today."

The Supreme Court ruling, however, left parts of the Arizona law standing, and Republicans at the state level vowed to press on.

Brewer, in a brief news conference, claimed the Arizona law had been "vindicated."

"The heart of the bill was upheld -- unanimously," she said, vowing to move forward with implementation and take on any remaining legal challenges.

Immigration laws in other states -- Utah, Alabama, Georgia, Indiana and South Carolina -- face an uncertain fate.

Alabama Gov. Robert Bentley said Monday that his state officials will "analyze" the opinion to determine its impact on Alabama but stressed that their law is "not identical" to Arizona's.

"I will keep my commitment to uphold and enforce Alabama's anti-illegal immigration law," he said. "The core of Arizona's anti-illegal immigration law remains."

The federal government's stated reluctance, though, to respond to state-level calls pertaining to immigration checks could make it difficult for Alabama and other states to carry out those laws. The Justice Department also announced Monday that it had set up a public hotline to report potential abuses linked to the Arizona policy.

President Obama, in a written statement, said the decision makes clear that a "patchwork of state laws is not a solution to our broken immigration system -- it's part of the problem."

Republicans agreed on the first part of that statement. With Arizona's law stripped of key provisions, they renewed their call for the federal government to step in with a comprehensive immigration solution -- and their criticism of Obama's handling of that task.

"Today's decision underscores the need for a president who will lead on this critical issue and work in a bipartisan fashion to pursue a national immigration strategy. President Obama has failed to provide any leadership on immigration," Republican presidential candidate Mitt Romney said in a statement.