Last Wednesday, after Pennsylvania Democrats picked Representative Joe Sestak over long serving (and recently Republican) incumbent Arlen Specter as their nominee for this Fall’s Senate race, the victor made the television rounds.

Sestak faced a bit of unfinished business, left over from months ago when Washington—and the White House—was betting on Specter to defeat the junior congressman. On February 18, Sestak appeared on a local cable political talk show, where he was asked if the White House had offered him an executive branch position in an attempt to lure him out of the race. Sestak said yes, and allowed that he had been offered a “high-ranking” position, but refused to give any details about the offer, including what the precise position was. When asked that day by Larry Kane, the show’s host, if it had been Secretary of the Navy, he responded with “No comment.”

Sestak has been asked about the matter many times since that day, and while he’s consistently maintained that the offer happened, he hasn’t volunteered much more information. The day after his win, CNN’s Rick Sanchez was only the latest to try to drill deeper.

“Did the president of the United States, did the White House approach you and offer you the secretary of the Navy position?” Sanchez asked. After Sestak dodged and said he didn’t have to “go beyond” what he’d already said, Sanchez tried again. “I just asked you a very direct question, give me a direct answer. Did the president, did the White House offer you the secretary of the Navy gig?”

Earlier that day, Sestak took a victory lap on Morning Joe, where Joe Scarborough, wrapping things up and thanking the new nominee for his time, offered this hagiography: “You took on the White House. You said no to the secretary of Navy job. You did it your way. You won. It’s a remarkable story. Congratulations.” And that weekend, when Sestak was on Meet the Press, David Gregory twice asked him if he’d been offered secretary of the Navy.

These interviewers were not at all exceptional. Many, many press accounts have speculated or assumed that the position at hand was secretary of the Navy.

There’s just one problem with this, as The Washington Post’s David Weigel pointed out Tuesday morning: what Sestak has said, combined with the timeline of events, makes it very hard to believe that the White House seriously offered him that particular position as an enticement to exit the Senate race.

Sestak was an oft-mentioned potential candidate for Specter’s seat before Specter became a Democrat on April 28. And he says he was being actively recruited by the White House to run against Specter up until the switch. But Obama nominated Ray Mabus, the former governor of Alabama and a Navy veteran, to be secretary of the Navy a month before Specter bolted his party. By that point, Sestak couldn’t possibly have shuffled in to replace Mabus as the nominee without someone asking obvious questions like: why did Mabus withdraw, and was it part of an improper deal?

Furthermore, shortly after taping Kane’s show, Sestak told Thomas Fitzgerald of the Philadelphia Inquirer that the offer, for whatever it was, had come in July 2009. Mabus had been confirmed by the Senate in mid-May.

Weigel’s post links a Post editorial from this morning that noted “the timeline” of the Mabus appointment made a Navy Secretary offer to Sestak “unlikely.” But Weigel’s post and today’s editorial are not the first time that the paper has cast cold water on the rumor. Way back on February 19, 2010, the same day that Fitzgerald reported on the yet-unbroadcast cable interview, Ben Pershing laid out the framework of the timeline, using Sestak’s official date of entry into the race:

Sestak, a retired Navy admiral, entered the Senate race last August, and he told Kane that the administration’s offer came in July. Ray Mabus was sworn in as Secretary of the Navy in June.

Clint Hendler is the managing editor of Mother Jones, and a former deputy editor of CJR.