As crowds of angry Bernie Sanders fans held rallies outside the Democratic National Convention on Monday in protest of Hillary Clinton's impending nomination, they were joined by another, lower-profile candidate hoping to win them over: Jill Stein, the presumptive presidential nominee for the Green Party.

Dr. Stein is inviting disgruntled Sanders-supporting Democrats to switch their allegiances to the Green Party, a third party known for supporting environmental and social justice causes. Some, fueled by a bitterness that grew over the weekend when leaked emails revealed apparent bias against Senator Sanders by the Democratic National Committee, are taking her up on her offer.

But political analysts say the obligation that many Democrats feel to vote for former Secretary of State Clinton to keep Republican nominee Donald Trump out of office presents significant challenges for third-party candidates hoping to take advantage of the presumptive Democratic nominee's unpopularity.

The question now for many Sanders supporters "becomes one of a trade-off," says James McCann, professor of political science at Purdue University, in West Lafayette, Ind., in a phone interview with The Christian Science Monitor. "Where do you set the threshold? How pure do you want to be, versus how meaningful do you want your vote to be?"

Some Sanders-supporters-turned-Stein-supporters say they have a moral obligation to vote with their conscience.

"There's one candidate for president that Bernie Sanders supporters can endorse, without feeling they’re rewarding a corrupt system, or succumbing to a lesser evil," writes columnist H.A. Goodman for the Huffington Post. "If she falls short of perfection, at least her goals are lofty and she remains independent of lobbyist influence."

At the same time, other Sanders fans say they have a moral obligation to vote for Clinton to stop a perceived greater evil: Mr. Trump.

"In order to make any sort of argument, you would have to explain how a vote for the Green Party isn't just a way that Donald Trump wins the White House," says Neil Sroka, communications director for the progressive group Democracy for America, to The Hill. "Even more importantly, it would potentially throw away the power that has been built over the course of this campaign for progressives within the Democratic Party."

But if there was ever a time for peak Green Party support among Democrats in this election year, it would be now, says Lawrence Jacobs, a professor of political science at the University of Minnesota. A combination of "combustible ingredients" including a "sense of betrayal by the DNC," the fact that "issues that Bernie Sanders has raised have not been adequately addressed," and "just the sadness and frustration of not winning" could work in a third party candidate's favor.

That support, however, Dr. Jacobs tells the Monitor, could – and most likely will – wane as November draws closer, as "there's a tendency to see the third party threat as larger in the beginning of a general election cycle than it turns out to be."

Disaffected Sanders fans on the path to eventually backing Clinton may have been pushed along by the keynote speech given by Sanders at the Democratic National Convention on Monday night, in which the Vermont senator stated that Hillary Clinton "must become the next president of the United States."

The speech, which was "as much of an unequivocal endorsement of Hillary Clinton as possible," did not send a message to Sanders' supporters to vote their conscience, notes Jennifer Lawless, a professor of government at American University, in Washington, D.C.

"Given that his supporters are so drawn to him and so dedicated to the cause ... it's unlikely that they're going to deviate from what he asks them to do," she tells the Monitor.

Comedian Sarah Silverman, a Bernie fan, voiced support for Clinton at the DNC, saying that she would vote for the presumptive Democratic nominee while continuing "to be inspired and moved to action by the ideals set forward by Bernie, who will never stop fighting for us."

Even with a less divisive Republican candidate and no perceived obligation to vote for the "lesser of two evils," the majority of Bernie fans would still likely end up voting for Clinton rather than supporting a third-party candidate like Stein, says Professor McCann.

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Though Donald Trump is "uniquely repulsive in various ways" in the eyes of the average Sanders supporter, he says, behind Trump's brash bravado is a platform with "very similar themes" to previous Republican platforms. With two such ideologically polarized parties, party loyalty typically beats out preference for individual candidates.

"I have to think that while the personality of the nominee matters a lot, we're talking about partisan competition here in large part," McCann says. "In other words, I would expect a lot of the Bernie types to come back to the Democratic fold, even if Trump hadn't been the nominee."