A call to Menendez's office Friday was not immediately returned, but his office released a statement insisting he'd done nothing wrong. The senator has pushed back vigorously against any accusations in the past, and is in the midst of a pitched battle with the Justice Department. Menendez claims that his actions and documents are covered by constitutional protections extended to members of Congress conducting their duties.

Menendez—who is in his second term as a senator, and served in the U.S. House from 1993 to 2006—is one of the White House's top frenemies in Congress, and any charges would add to an already contentious relationship. For the last two years, while Democrats held the Senate, he was chair of the Foreign Relations Committee. A staunch backer of the Israeli government, he repeatedly moved to strengthen sanctions against Iran while negotiations over that country's nuclear program were ongoing, much to Obama administration's annoyance. (Menendez and other Democrats eventually backed down.) As a Cuban-American, he has also been a fierce critic of Obama's move to normalize relations with the Communist government in Havana. And he clashed with the White House over the Authorization for Use of Military Force against ISIS.

There are plenty of waggish jokes here about how corruption is standard-operating procedure, but Menendez has been part of an unusual slow-burning scandal. Just before the November 2012 election, the Daily Caller reported—in what looked like a botched oppo-dump—that Menendez has traveled to the Dominican Republic with Melgen, where prostitution is legal, and hired prostitutes there. The story backfired. Menendez cruised to reelection, and the FBI ended up investigating the source of the allegations. But the story seems to have brought more attention to Menendez, too, as reporters and investigators started to look into the senator's dealings.

It's not Menendez's first scrape with the law—in 2006, a young Republican U.S. attorney was accused of launching an investigation into Menendez right before an election in an attempt to sway the result. The investigation went nowhere, but the prosecutor, Chris Christie, did. If Menendez were forced to step down or was removed from office, Christie—now governor and himself dogged by scandal—would have the chance to fill the seat temporarily, until a special election was held. That would allow Republicans to pick the seat up, at least temporarily. But the Garden State hasn't elected a Republican to the U.S. Senate since 1972.