Homeland Security Secretary Janet Napolitano’s decision to leave the Cabinet this fall means President Barack Obama will have to find a replacement just as deliberations over an immigration overhaul may reach their peak.

Many Republicans have faulted Napolitano and Obama for moving administratively to remove the threat of deportation from over the heads of many young immigrants brought into the country illegally by their parents rather than wait for Congress to pass legislation.

GOP lawmakers have frequently accused DHS of exceeding its legal authority by allowing its immigration enforcement agencies to practice “prosecutorial discretion” that focused apprehension and deportation resources on violent criminals and other high-profile targets instead of those whose offenses were limited to violating immigration law.

Sen. Jeff Sessions, R-Ala., said that policy will define her record. “Secretary Napolitano’s tenure at the Department of Homeland Security was defined by a consistent disrespect for the rule of law,” he said in a written statement. “The resignation of Secretary Napolitano should refocus the attention of Congress on its first task: to ensure that the executive branch faithfully carries out the laws of the land. The most significant obstacle to immigration reform remains President Obama’s selective enforcement of the law.”

Napolitano announced Friday she is resigning as secretary, effective early this fall, to take the job as president of the University of California system.

“For more than four years I have had the privilege of serving President Obama and his Administration as the Secretary of Homeland Security. … I thank President Obama for the chance to serve our nation during this important chapter in our history, and I know the Department of Homeland Security will continue to perform its important duties with the honor and focus that the American public expects,” she said in her statement.

Obama thanked Napolitano for her service, highlighting her work after the Joplin tornado and Hurricane Sandy, as well as her border security initiatives.

“Since day one, Janet has led my administration’s effort to secure our borders, deploying a historic number of resources, while also taking steps to make our immigration system fairer and more consistent with our values,” he said in a written statement. “And the American people are safer and more secure thanks to Janet’s leadership in protecting our homeland against terrorist attacks. I’ve come to rely on Janet’s judgment and advice, but I’ve also come to value her friendship. And as she begins a new chapter in a remarkable career of public service, I wish her the best of luck.”

Napolitano plans to remain at the department into September, and the administration has no personnel changes in mind until she leaves. The former Arizona governor called the homeland security job the highlight of her career.

“The Department has improved the safety of travelers; implemented smart steps that make our immigration system more fair and focused while deploying record resources to protect our nation’s borders; worked with states to build resiliency and make our nation’s emergency and disaster response capabilities more robust; and partnered with the private sector to improve our cybersecurity.”

“After four plus years of focusing on these challenges, I will be nominated as the next President of the University of California to play a role in educating our nation’s next generation of leaders,” she added.

Napolitano is the longest-serving secretary in the department’s short history. In Washington, she has emphasized her connection to the Southwest and border security, and became one of the Obama administration’s leading advocates for a comprehensive overhaul of the immigration system.

In numerous speeches and testimonies before Congress, she has highlighted the buildup of the Border Patrol and its supporting agencies over the past decade, calling the Southwest border the most secure it has ever been.

That assertion has been one of the most contentious issues between the administration and Republican lawmakers, particularly during immigration overhaul discussions. While Napolitano and other officials have pointed to declining apprehensions in the Southwest and other signs that fewer people are trying to cross, GOP members — particularly those from Southwest states — have called the administration’s claims untrue, and continued to do so Friday.

“The border is not secure, and the threat of terrorism is not diminishing,” House Homeland Security Chairman Michael McCaul, R-Texas, said in a statement on Napolitano’s departure. “The vision and actions of the Department must reflect that reality.”

McCaul called for the administration to appoint a replacement “who does not underestimate the threats against us, and who is committed to enforcing the law and creating a unified Department. Ten years after the creation of the Department, it is critical that its mission isn’t undermined by politics or political correctness.” While he noted that he disagreed with Napolitano on the border and other issues, he said he respected her for her service.

Sen. John McCain, R-Ariz., also sounded a respectful note. “Janet Napolitano has served our nation with honor over the last four years as Secretary of the Department of Homeland Security — one of the toughest and most thankless jobs in Washington,” he said.

“We have had our share of disagreements during her time as Secretary, but I have never doubted her integrity, work ethic or commitment to our nation’s security. The people of Arizona can be very proud of our former Governor’s service, and I wish her all the best as she assumes leadership of the nation’s largest public university system,” he added.

Although Napolitano has not always seen-eye-to-eye with Capitol Hill Democrats — several have expressed reservations about the nationwide expansion of Secure Communities, a program that allows federal officials to match fingerprints taken during local police bookings with those on file in immigration databases — she has generally had a more cordial relationship with them.

Bennie Thompson, D-Miss., ranking member on the House Homeland Security Committee, called her a “steady hand helping lead the 240,000 men and women who serve in the Department through natural disasters and a diverse matrix of threats,” and said she deserves credit for helping to unify the 10-year old department, which was largely cobbled together out of 22 existing agencies.

“I call upon the President to act quickly and nominate a qualified replacement for this critical role,” he said in a written statement. “Similarly, I urge my colleagues in the Senate to move as swiftly in confirming Secretary Napolitano’s successor as they did in confirming her. The country needs a well-qualified, proven leader to direct this Department given the wide range of threats, man-made and natural, that our Nation faces.”

Republicans also criticized the department under Napolitano’s leadership for drastically cutting down on worksite raids of businesses that employ illegal immigrants.

Obama and Napolitano have, however, emphasized their immigration enforcement record. Under Napolitano, DHS posted increasingly high annual deportation numbers, reaching 391,953 in fiscal 2011.

Napolitano also presided over a controversial time in the Transportation Security Administration’s history, as it began a large-scale deployment of full-body scanners to airports after the 2009 “underwear bomber” attempt to bring down an airplane over Detroit. The “naked scans” originally generated by the machines, along with pat-downs administered by officers, provoked a backlash from the traveling public, civil liberties groups and many lawmakers.

Napolitano defended the TSA’s policies, but has said the agency needs to do a better job communicating with the public. Over the past two years, the TSA has installed privacy filters on its airport body scanners.

Far less controversial was her leadership during natural disasters. Efforts by DHS and the Federal Emergency Management Agency to coordinate disaster relief before superstorm Sandy struck the East Coast last year and respond to the resulting devastation drew praise from many members of Congress.