But how likely is this to go all the way to the convention floor itself?

In an interview with me today, top Sanders adviser Tad Devine shed a bit more light on this question: He conceded that if Sanders does not “significantly” close the current pledged delegate gap with Clinton, it will be borderline “impossible” to persuade super-delegates to switch from Clinton to Sanders.

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“I think it’s going to be very, very difficult for us to persuade large numbers of super delegates to move if we don’t significantly make progress in the pledged delegate count,” Devine told me.

“We believe we have a shot at winning if we make great progress between now and then,” Devine also said. “We concede that if we don’t make that progress, then the task of moving all these super delegates is practically impossible.”

To be sure, Devine declined to be too specific about what would constitute the “significant” or “great” progress in the pledged delegate count that the Sanders campaign has to achieve, in order to have a plausible shot at flipping super delegates. Asked to specify this, Devine said: “I’m not going to put an exact number on it. We’ll know it when we see it.”

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Still, in one sense, this is an important concession from Devine. In effect, what he is saying is that the quest for super-delegates will be a non-starter unless Sanders makes big gains in closing the pledged delegate gap. Following this logic to its natural conclusion, if that doesn’t happen, it should become more likely that the Sanders campaign will not push this all the way to a battle at the convention, meaning he might concede in June, after the voting is done, and help to unify the party before the convention.

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For now, then, Sanders’s hints at a contested convention are probably designed to keep his supporters engaged in hopes of pulling off a major shift in the remaining dozen contests, or if that doesn’t happen, to further build his national constituency in hopes of leveraging some influence over the party’s agenda heading into the general election.

Right now, Clinton leads Sanders by 321 in pledged delegates. She has 1,641, and Sanders has 1,320. Sanders must win 65 percent of the remaining pledged delegates to get a majority of them; she must win only 35 percent of them to get to a majority. This does not include super-delegates: Add those in, and Clinton leads by 790 overall delegates; Sanders would have to win 81 percent of overall delegates to get the 2,383 overall delegate majority needed to secure the nomination.

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As Devine says, Sanders must first close the gap dramatically among pledged delegates, in order to have any shot at winning over super-delegates later. (They simply aren’t going to switch, but let’s concede the point, just for the sake of argument.) How possible is that?

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To do it, Sanders might have to win around 60 percent or more of the remaining vote (whoever wins in Indiana today, the two are likely to come close to splitting the delegates there). Dave Wasserman, who tracks delegate math for the Cook Political Report, tells me that big delegate gains for Sanders are highly improbable — indeed, it’s more likely, in his view, that her lead among pledged delegates will expand by the time the voting ends in mid-June.

“Sanders would be lucky to maintain the delegate deficit he currently suffers,” Wasserman says. “Clinton will significantly expand her raw delegate margin by June 14th. Based on demographic models of the voting so far, Clinton is likely to beat Sanders by comfortable margins in California and New Jersey, which are home to most of the delegates that remain at stake.”

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Devine acknowledged that if she does expand her pledged delegate lead, it will be “practically impossible” to prevail on super-delegates to switch. But Devine said the campaign still sees the possibility of a home stretch in which “we win most of the states and most of the delegates between now and the end,” with some victories proving to be “impressive.” If so, “all of these things are factors to take into consideration,” he said.

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If Sanders does not make big gains in closing the pledged delegate count, by Devine’s own admission, the case to super-delegates becomes far-fetched. At that point, would Sanders concede in June, after all the voting is done, rather than carry the fight to the convention floor in Philadelphia? Asked if there is a scenario in which Sanders does refrain from a convention fight, Devine said: “I don’t want to speculate about what our position will be in six weeks.”