WASHINGTON (AP) — A high-profile bipartisan task force chaired by former governors and Cabinet secretaries endorsed eventual citizenship for immigrants living in the U.S. illegally as part of a package of recommendations Thursday.

The proposals were aimed at influencing the debate on immigration, with Congress on a five-week summer recess and Senate-passed immigration legislation stalled in the GOP-controlled House.

The immigration task force, convened by the Bipartisan Policy Center, is co-chaired by former Secretary of State Condoleezza Rice and former Mississippi Gov. Haley Barbour, both Republicans; along with former Pennsylvania Gov. Ed Rendell and former Housing Secretary Henry Cisneros, who are Democrats.

The group's recommendations included calling for an independent commission to measure border security; a path to citizenship for the 11 million people living here without legal permission; and a strong visa program to bring foreign workers into the economy, coupled with stricter penalties for employers that hire or exploit workers living here illegally.

"We find it's possible to reach common ground on some basic principles that do get a broad agreement from people coming at the problem with different political perspectives," Michael Chertoff, homeland security secretary under President George W. Bush and a member of the task force, said on a conference call with reporters.

"We're hopeful that the country, when we all take a deep breath over the summer, looks at how broken the system currently is (and) will see that the value of coming up with a broad consensus reform far outweighs the benefit of the status quo."

Several of the recommendations track generally with the Senate bill, which aims for border security, improved legal immigration and workplace enforcement, and eventual citizenship for the millions already here illegally.

But the task force criticized the Senate's approach to border security, a last-minute compromise aimed at securing Republican votes that sets aside $46 billion to double the number of agents along the U.S.-Mexico border, to complete hundreds of miles of fencing and to beef up technology from drones to helicopters to watchtowers. The approach "does not provide outcome-based border-security metrics that are trustworthy and verifiable," the report said, calling for the creation of such measures that would be audited by an independent commission and made public.

Similar criticism is sometimes heard from House Republicans, who say that border security must be tackled before any other step is taken on immigration but generally dislike the Senate bill.

The task force recommendations amount to the latest example of establishment Republicans promoting comprehensive solutions on immigration in the face of balking by the conservatives who control the House. It comes as advocates nationwide, from business to labor to evangelicals, seek to exert pressure on House Republicans to take action once they return to Washington in September.