Jimmy Kimmel relayed an invitation from Sanders to Trump. Later, on Twitter, Sanders wrote, “I am delighted that @realDonaldTrump has agreed to debate. Let’s do it in the biggest stadium possible.” Photograph by Randy Holmes / ABC via Getty

Update: On Friday afternoon, Trump backed out of appearing with Sanders. He said he would wait and debate whichever candidate emerged from the “rigged” Democratic primary.

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That’s the pitch that has been circulating on social media for the past couple of days, and Sanders himself has done some of the pitching. “Game on. I look forward to debating Donald Trump in California before the June 7 primary,” the Vermont senator tweeted on Wednesday night. That came shortly after Jimmy Kimmel, the host of “Jimmy Kimmel Live,” relayed an invitation to Trump, which he said had come from Sanders, to debate the Democratic insurgent. “If he paid a nice sum toward a charity, I would love to do that,” Trump replied.

It wasn’t immediately clear how serious Trump was: some sources close to him told reporters that he was just kidding. But Sanders appeared to be offering in earnest, prompted in part by the Clinton campaign’s decision, announced Monday, not to follow through on an earlier pledge to debate him in California. On Thursday, he tweeted, “I am delighted that @realDonaldTrump has agreed to debate. Let’s do it in the biggest stadium possible.” Sanders delivered the same message in a speech, and his campaign manager, Jeff Weaver, told CNN, “We are ready to debate Donald Trump. We hope he will not chicken out. I think it will be great for America to see these two candidates and the different visions they have for America going forward.” On Friday, Sanders tweeted a link to a petition gathering support for a debate with Trump.

It’s not entirely clear what the Sanders campaign is up to here. The most straightforward explanation is that it thinks debating Trump could shake up the race in California, where the poll averages show Clinton retaining a double-digit lead over him, and that a victory for Sanders in the Golden State would upend the Democratic contest. (Indeed, a poll released Wednesday by the nonpartisan Public Policy Institute of California has the race within the margin of error.) Even if Sanders did come out ahead of Clinton there, he would almost certainly remain unable to overtake her in the pledged-delegate count. But getting defeated in California would undoubtedly be a blow to Clinton, and Sanders could conceivably seize upon it to try and persuade some superdelegates to change sides.

Another possible explanation is that the Sanders campaign expects Trump to change his mind and drop out. With Trump now focussed on uniting the Republican Party behind him, at least some of his advisers will likely tell him not to risk debating Sanders, who would doubtless go after him with merry abandon. If Trump decided not to take up the offer, Sanders could say that he had intimidated the presumptive Republican nominee, which would also give his campaign a lift.

A third theory is that the overture to Trump was designed to put pressure on Hillary Clinton to follow through on her earlier pledge to debate Sanders in California. It isn’t entirely clear who would come out the winner in a Trump-Sanders debate, but it seems likely that Clinton would lose, since she wouldn’t be there to defend herself against any attacks. Her absence from the stage would be palpable.

If this is what Sanders is doing, it’s a cynical move, though Clinton’s refusal to debate Sanders in the largest state in the country was also cynical: the Clinton campaign didn’t see any advantage in another head-to-head session, so it refused to participate. Now Sanders has raised the stakes, saying that he’ll debate Trump instead.

But what if Clinton stands her ground and Trump does show up? Some Democrats fear that a Trump-Sanders encounter would turn into the sort of media circus that Trump revels in, and that it would only heighten the divisions in the Democratic Party at a time when it needs to unite against Trump. If a debate did take place, it would certainly get good ratings, and Trump would surely use the occasion to bait Clinton, appeal to the “Bernie or Bust” contingent, and generally try to sow more dissension in the Democratic Party.

“Sanders should think long and hard about giving Trump a forum,” Chris Kofinis, a Democratic strategist who was formerly the chief of staff to Democratic Senator Joe Manchin, told Reuters. “It crosses a line, but apparently in this election there is no line.” Brad Bannon, another Democratic operative, told The Hill, “This is just an unbelievable spectacle. It really upstages Hillary at a critical time for her. The Clinton folks must be furious.”

When CNN’s Wolf Blitzer asked Clinton on Thursday about the possibility of a Trump-Sanders debate, she dismissed it, saying, “I don’t think it’s serious. It’s not going to happen.” Perhaps not. But many of Clinton’s supporters will regard Sanders’s willingness to even countenance such an event as another sign of disrespect for a front-runner who has, according to FiveThirtyEight, a lead of more than 2.9 million in the popular vote, including the caucus states.

And that means the bitterness between the two sides is likely to increase. In fact, it has already done so. On Twitter on Thursday, Sanders supporters revelled in the prospect of a debate with Trump, while Clinton supporters accused Sanders of being a sore loser, and even of teaming up with Trump to undermine Clinton. “Frankly, the fact that Hillary has achieved a level of visibility, power, and influence that few women ever have makes me all the more furious that two men are still trying to show, ‘jokingly’ or seriously, they can gang up to push her around at will, that they don’t respect her agency or her right to say no,” Melissa McEwan, the founder of Shakesville, a feminist blog community, wrote at the pro-Clinton Blue Nation Review. “By every conceivable metric, Bernie failed this test. Badly.”