WASHINGTON - President Obama received Arizona Gov. Jan Brewer in the Oval Office on Thursday, but the two could not bridge the gulf that divides them - and the country - over illegal immigration and border security.

Brewer, who has signed a law requiring Arizona police to check the status of people they suspect are illegal immigrants, wants more federal resources - troops, helicopters, aerial drones, and fences - devoted to controlling her state's border with Mexico.

She said she got no commitment from Obama, other than a promise of better communication.

"I am encouraged that there is going to be much better dialogue between the federal government and the state of Arizona now," she told reporters outside the White House.

In a nod to those seeking more enforcement, Obama last week promised to spend an additional $500 million and send 1,200 National Guard troops to the border.

The president believes, however, that enforcement should accompany a comprehensive change in immigration law.

He supports the latest Democratic version of such a bill, which requires a tamperproof Social Security card, a temporary-worker program for foreigners, and a path to legalization for the 11 million immigrants already here. Such steps, backers say, are designed to close down the market for undocumented labor that draws people to cross the border illegally.

Brewer and other Republicans say they can't back an immigration overhaul until the border is more tightly controlled.

"I want the border secured first," she said. After the last immigration rewrite, in 1996, she said, "amnesty was bestowed upon people, but we never secured the borders."

Brewer, who is up for reelection, has said her state is "under siege" from border crime, though statistics don't bear her out. Crime rates are stable or down along the U.S. side of the border, even as an epidemic of drug violence wracks the Mexican side.

"Crime is down in Arizona," Brewer acknowledged in an interview with CNN's John King. "[But] the fact of the matter is, if you're living in Arizona and you are living in the areas that are severely impacted, you are faced with it on a daily basis."

Certain types of crime, particularly kidnappings and robberies among those involved with illegal drugs, have increased in Arizona in recent years, said Dennis Burke, the U.S. attorney for the state.

Brewer said Obama declined to discuss whether the Justice Department would challenge the constitutionality of the Arizona law, which the president has said could lead to racial profiling.

"He was going to basically leave that up to the Department of Justice," she said.

Brewer requested the meeting with Obama, White House spokesman Robert Gibbs said. Asked why the president agreed to it, Gibbs said: "I don't think you're going to deal with comprehensive immigration reform and circumstances along the border without dealing with Arizona."

The Arizona law expressly prohibits profiling, and Brewer has said it represents a reasonable response to what she says is the failure of the federal government to enforce immigration law.

Several polls have shown that a majority of Americans support the law. A survey conducted by Quinnipiac University from May 19-24 found that 51 percent of Americans approve of the law while 31 percent disapprove.

Homeland Security Secretary Janet Napolitano has argued that the Southwestern border is as secure as it's ever been, a position echoed by Bush administration officials, including Thad Bingel, a former chief of staff at Customs and Border Protection.

The size of the Border Patrol has doubled to 20,000 since 2004. Apprehensions of illegal immigrants are at their lowest levels in years, suggesting that the number of illegal crossers has plummeted.