President Obama arrives to address law enforcement leaders from across the country in the Eisenhower Executive Office Building in Washington on Tuesday. (Pool photo by Win McNamee/Via European Pressphoto Agency)

The Obama administration is likely to overhaul a program that allows the federal government to partner with local law enforcement agencies to identify illegal immigrants for deportation, police chiefs said Tuesday.

Several municipal police chiefs who attended a meeting at the White House said that Homeland Security Secretary Jeh Johnson indicated he was planning to revamp the program, known as Secure Communities.

Immigrant advocates say the program has improperly targeted undocumented immigrants who are arrested for relatively minor violations and have no prior record other than being in the country illegally. Johnson is conducting an internal review of the administration’s immigration enforcement policies at the request of President Obama, who has been under increasing pressure from advocates to stem deportations.

Johnson told the police chiefs that “Secure Communities had a false start and a lot of people did not understand what it is,” said Art Acevedo, the police chief of Austin. “The sense I got is that we are going to see a reboot of Secure Communities, and once that comes out, you’ll see a singular focus in state and local counties on violent criminals.”

The police chiefs said Johnson did not say when he will announce the results of his review or potential changes. A Department of Homeland Security spokesman declined to discuss details from the meeting.

The Obama administration is trying to keep pressure on Republicans in the House to support a comprehensive overhaul of immigration laws, an effort that has been stalled in that chamber since the Senate approved a bipartisan plan last June.

The White House believes the next few months before the House takes summer recess in August are critical. Obama said during a brief appearance with the police chiefs that time is running out.

“We’ve got this narrow window,” the president said. “The closer we get to the midterm elections, the harder it is to get things done around here. . . . So we’ve got maybe a window of two, three months to get the ball rolling in the House of Representatives.”

House GOP leaders have said they plan to pursue smaller-scale immigration bills, and some high-ranking Republican Party officials believe it would be beneficial for the party to address immigration reform in advance of the 2016 race for the White House.

U.S. Chamber of Commerce President Thomas Donohue joked Monday that the GOP “shouldn’t bother” to field a presidential candidate if it does not pass a broad immigration bill, given the growing clout of Latinos and Asian Americans.

But House Republican leaders have been unwilling to move forward in the face of opposition from more conservative elements of their caucus. On Tuesday, a spokesman for Speaker John A. Boehner (R-Ohio) repeated the GOP contention that Obama has lost their trust that he “will actually enforce the law as written.”

Republicans have pointed to administrative changes to enrollment regulations in the president’s health-care law and a 2012 administrative decision to stop deporting some young illegal immigrants.

The rift has complicated the administration’s attempts to address the mounting concerns of immigrant advocates, who have called on Obama to use his executive power to further stem deportations of the estimated 11 million to 12 million illegal immigrants.

Secure Communities, begun in 2008 under President George W. Bush, allows local police departments to share information on arrestees with the federal Immigration and Customs Enforcement agency to determine whether they are eligible for deportation.

Defenders of the program say it is designed to help federal agents identify violent criminals and repeat offenders. But detractors say the program has been abused to target people arrested on traffic violations and other lower-level offenses. Some municipalities, including Philadelphia and Baltimore, have scaled back their cooperation with ICE.

“Our stance is, if ICE and DHS want to partner with us to go after people who do harm to the citizens and residents of our communities, we’ll take their support and efforts any day of the week,” Acevedo said. “But if they want to focus on people’s immigration status who are otherwise law-abiding, we are not interested.”