Betsy Hodges is running for re-election as mayor of Minneapolis this year on a fairly progressive record. She's devoted some $40 million to affordable housing, put an emphasis on care for young children and signed an ordinance mandating that employers provide paid sick leave.

Nonetheless, Hodges faces several serious challengers running to her left. Hodges has opened herself up to progressive criticism due to her shifting positions on a prospective minimum-wage increase and handling of a high-profile police shooting.

"Even though she's the most progressive mayor in Minnesota, most of her rivals are to the left of her," says Larry Jacobs, a political scientist at the University of Minnesota. "There's no doubt there's a kind of Robespierre moment in the Democratic Party, where if you're not sufficiently pure, you're suspect."

Robespierre was a leader in revolutionary France who launched a "reign of terror" to enforce political purity. Democrats are not going anywhere near that far. But there's no doubt progressives are challenging party leaders and officeholders not just to oppose President Trump at every turn, but to adhere to liberal positions across the board.

Parties tend to return to their bases after losing the presidency, says Lara Brown, a political scientist at George Washington University. "What opens up is this huge strategic debate about what should we stand for and who should be our leader."

Indeed, contemporary parties that have suffered losses seem to go through a phase where there's an internal argument about identity. Much as the Republican Party became more conservative following the election of President Barack Obama, Democrats now are insisting that their leaders adhere strictly to liberal doctrine, threatening to punish officeholders who break from orthodoxy. New progressive groups such as Our Revolution and Indivisible rose from the ashes of the party's defeat last year, recruiting liberal candidates and holding elected Democrats' feet to the fire.

There was a symbolic fight along these lines immediately after the election, when the Democratic Party picked Tom Perez as its new chair. Because he had served in the Obama administration, Perez was seen as the "establishment" choice over progressive Congressman Keith Ellison, who happens to represent Minneapolis.

The framing of that debate has already colored other party contests.

In Virginia, for instance, former Congressman Tom Perriello is challenging Lt. Gov. Ralph Northam for the gubernatorial nomination in next month's primary, painting himself as the more progressive choice on economic issues. This past weekend, former congressional candidate Kathleen Matthews was selected to chair the Maryland Democratic Party, with her opponent complaining she was an establishment choice who would do things the same old way.

Elected Democrats such as New York Gov. Andrew Cuomo also find themselves castigated from the left, even when they've put a lot of progressive points on the board on issues such as environmental protections, minimum wage and gay rights. "The dynamics within the Democratic Party have created a demand for more progressive governance," says Karen Scharff, executive director of Citizen Action of New York, a liberal advocacy group.

Arguments about party orthodoxy spilled out into the open in yesterday's election for mayor of Omaha. Democrat Heath Mello launched a strong challenge to GOP Mayor Jean Stothert, but he lacked the full backing of his party. Prompted by votes Mello had cast in the Nebraska Legislature against abortion rights, party chair Perez stated that all Democratic candidates had to respect women's reproductive rights.

That stance was too doctrinaire for Nancy Pelosi, the Democratic leader in the U.S. House. She said last week that the party shouldn't demand that candidates pass a litmus test on any particular issue.

Now Pelosi herself has drawn a challenge from the left, an environmental attorney named Stephen Jaffe. "Jaffe suggests Pelosi is not liberal enough or, for that matter, even a true liberal, a proposition that would be dismissed as outlandish anywhere other than San Francisco," noted the Los Angeles Times.

Jaffe won't give Pelosi a serious scare, but his challenge illustrates two of the main dynamics driving this push for progressive purity.

Democratic voting strength and the party's remnants of power are not exclusively, but mainly limited to the major cities, college towns and the coasts. If you live in a blue enclave, you're more likely to believe that a progressive vision provides not just a winning but a necessary message.

"New York should be a triple-blue state, given our makeup," Scharff says. "It's been true forever that New York could be more of a leading progressive state than it's been, and it's more true than ever now that New York has to play that role, taking the lead in the way other states are leading in a moment when we desperately need state governments to protect us against a right-wing federal government."

A number of progressive candidates who are now lining up, including Jaffe, were energized by the presidential campaign of Bernie Sanders. Many Democrats now believe Sanders, a self-described democratic socialist, could have succeeded against Trump where the more moderate Hillary Clinton failed.

It's the mirror image of Republicans who complained that they lost to Obama because their presidential nominees weren't conservative enough. Some progressive activists have openly compared themselves to the Tea Party, which succeeded in pulling the GOP to the right. "What happens is the loss opens up the fractures [within the party] that had been forming, that get papered over when you have the presidency," says Brown, the George Washington University professor.

It's already clear that progressives aren't going to win every battle they pick. But Michael Quinn Sullivan, who runs a conservative advocacy group called Empower Texans, gives Democrats credit for having the "nerve" to hold a discussion about what their convictions are and how they have to stick to them. "The Democrats are definitely in a state of existential crisis," he says.

His warning for the other side is that, by insisting on orthodoxy among elected officials, progressives risk not only chiding candidates, but putting off potential supporters. "That's going to translate to voters as saying, 'if you have beliefs that are at odds with the party platform, you're not welcome any more,'" Sullivan says.

It's clear from the amount of ongoing protests and striking fundraising numbers being posted by traditional party organizations and the new groups that Democrats have been highly energized by the Trump presidency. Getting their core supporters excited about voting is the first step in returning to power -- and may be enough to propel the party to big victories in the midterm elections next year.

But regaining strength on a national basis requires more than firing up the base. Winning requires building coalitions, an act that by its nature means making peace with individuals and groups who hold different perspectives. Politics is all about creating as big a movement as possible among actors whose beliefs overlap, but don't line up entirely. "This quest for purity at the end of the day is a self-defeating strategy, because you end up narrowing your appeal, not increasing it," Brown says.

Partisans on the left may argue that the presidency was lost because people who shared their ideological beliefs were insufficiently motivated by Clinton's candidacy to turn out to vote. There may be some truth to that, but Brown warns that parties can seldom recover voters whose affections they've lost. "You have to go forward and start pushing into the opposing party's base," he says, "where they have started to ignore their supporters."