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That will likely set up another controversial nomination battle just as the House is debating immigration bills — and the next nominee will likely have to answer tough questions about how to measure illegal immigration across the southern border.

It could also end up being the first major nomination test under new Senate rules if Democrats move ahead next week with the so-called “nuclear option” to change rules to eliminate filibusters of executive branch appointments.

Ms. Napolitano, who the Drudge Report made notorious by dubbing her “Big Sis,” has been a frequent target of attacks from both the right and the left over the TSA’s actions.

And her department ignited a firestorm when it signed contracts to buy hundreds of millions of rounds of ammunition, spurring gun-rights activists to accuse her of trying to push up prices for average consumers.

Ms. Napolitano later admitted she had been slow to shoot down the reports because she thought they were so preposterous that nobody would believe them. But members of Congress, whose offices were getting flooded with calls, launched several investigations into the ammunition situation.