In the wake of the Supreme Court decision to uphold Arizona’s law allowing police to check the immigration status of those they detain, an overwhelming majority of Americans say they want to see their own states enact the same kinds of laws.

The latest Washington Times/JZ Analytics survey, released Monday night, found about two-thirds of all likely voters would like to see their own police be able to check immigration status during routine traffic stops. Support was high across most demographics, including self-identified Republicans and independents, and even Hispanics favored the policy by a 55 percent to 41 percent margin.

The Supreme Court last month struck down most of Arizona’s 2010 law that tried to create state penalties for illegal immigration, but said states and localities can empower their police to check the immigration status of those they detain during their routine duties.

Justices agreed the checks were legal in theory, though they said that could change if police use them in a way, such as detaining someone for too long, that violates other rights.

In the poll, voters were given arguments for and against the law, then asked if they wanted to see their own communities enact something similar. Overall, 50 percent of voters said they “strongly” agreed with enacting that law, and an additional 17 percent “somewhat” agreed. Just 29 percent strongly or somewhat disagreed, and the rest were uncertain.

John Zogby, who conducted the poll for The Times, said voters do not appear to be worried about getting detained themselves.

“I think what a majority here are saying is that projected on the ‘other,’ it doesn’t seem like a bad thing, and it doesn’t seem like an invasive thing to do,” he said. “It seems like something that can be efficient and at the same not hurt the majority of law-abiding citizens.”

President Obama and Attorney General Eric H. Holder Jr. have both said they thought this kind of statute, which critics call the “show your papers” law, would lead to racial profiling — though Arizona police have been instructed that race alone is not sufficient reason to suspect someone may be illegally in the country.

But in the courts, the Obama administration only argued over federal versus state powers, and avoided suing over racial profiling.

Since the ruling, officials have signaled that’s still an option, with Mr. Holder telling the National Council of La Raza’s annual conference this week he’ll keep a close eye on the way Arizona and other states implement the statute.

A handful of states have followed Arizona’s lead and enacted similar police powers, but some jurisdictions have gone the other direction.

On Tuesday, Chicago Mayor Rahm Emanuel announced an ordinance he said would make sure police know they don’t have to turn illegal immigrants over to federal authorities.

The move won applause from Rep. Luis V. Gutierrez, Illinois Democrat and a chief advocate for immigrant rights, who contrasted it with the get-tough policies others are turning to.

“In Arizona, they deal with this reality by enacting laws to sanction racial profiling and by condoning the irrational acts of cowboys — sometimes ones who happen to be sheriffs and carry guns — and set them loose on immigrants or anyone who looks or sounds like an immigrant,” Mr. Gutierrez said. “In Chicago, we do things a little differently because we put public safety above political stunts, and we put creating a united, cohesive society over trying to draw dividing lines or driving political wedges.”

The Times/JZ Analytics poll surveyed 800 likely voters by live phone interview between Friday and Sunday. The results are weighted for demographics, and the poll has a margin of error of plus or minus 3.5 percentage points.

The survey asked how voters think the estimated 11 million illegal immigrants now in the U.S. should be handled, and found a strong plurality want them to go home without being offered a special path to citizenship from within the U.S.

Overall, 49 percent said illegal immigrants should be “given a chance to get their affairs in order [and] then sent home, where they can apply to return through regular immigration channels.” That’s up 4 percentage points from the last TWT/JZ Analytics Poll in May.

Support for a pathway to citizenship from within the U.S. dropped 4 points, down to 29 percent, while a third option — letting illegal immigrants stay in the U.S. but without the chance for citizenship — was static at about 9 percent.

Both Republicans and self-identified independents strongly favored having illegal immigrants go home, while Democrats were more likely to want a path to citizenship.

Mr. Obama has called for a path to citizenship and last month issued a directive canceling deportations for most illegal immigrants age 30 and under.

Presumptive Republican presidential nominee Mitt Romney has staked out the strictest immigration-enforcement platform of any major-party candidate in recent years, praising state laws such as Arizona’s and calling for stricter enforcement at the federal level.

He has said, however, that he would allow illegal immigrants who join the U.S. military to be offered a path to citizenship.

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