The symmetry was irresistible. Last weekend, as Ted Cruz almost blew up the budget deal over immigration and Elizabeth Warren almost blew it up over banking regulations, pundits seized upon an analogy. Both senators are articulate, ideological, media-savvy, beloved by party activists, and problematic for party leaders. Thus, Warren is the Cruz of the left.

Bad analogy, argues Vox’s Matthew Yglesias, noting that it’s Cruz and the GOP that want “to use government funding as leverage to undo policy measures Democrats enacted in the 111th Congress.” Warren just doesn’t “want to pay the ransom.” The Washington Post’s Sean Sullivan is dubious too, noting that Mitch McConnell and John Boehner dislike Cruz a lot more than Harry Reid and Nancy Pelosi dislike Warren.

But there’s another, more fundamental, difference. Cruz deepens America’s red-blue divide. Warren could scramble it.

Think about Cruz’s highest-profile crusades: against Obamacare, against Obama’s executive action on immigration, against raising the debt ceiling, against gun control. They all exhilarated conservative activists and repelled their liberal counterparts.

With Warren it’s different. Her signature crusade is against the economic and political power of Wall Street. And it’s a crusade that appeals to elements of the American right. Most conservatives don’t like big banks either. In 2012, Pew found that while 78 percent of Democrats said Wall Street “only cares about making money for itself,” 66 percent of Republicans did too. Sixty percent of Mitt Romney voters said there was “too much power in hands of a few big companies.” And according to a 2013 Huffington Post poll, Republicans agreed that “banks and financial institutions have grown too big and powerful” by a margin of almost two to one.

Warren’s answer to this is threefold. First, she wants tougher banking regulation, and since this means empowering federal bureaucrats, conservatives are overwhelmingly opposed. But Warren’s other solutions hold more bipartisan appeal. She wants to break up the big banks. Perhaps because this does not imply a permanent expansion of government oversight, conservatives are more sympathetic. According to The Huffington Post, a plurality of Republicans favor “a law that would cap the size of banks in the US and force the largest banks to break into smaller units.” Finally, Warren opposes bank bailouts. And because this means less government intervention, not more, conservatives find it wildly appealing. It was opposition to George W. Bush’s Troubled Asset Relief Program that helped create the Tea Party. According to a 2012 Harris poll, Republicans still overwhelmingly consider bank bailouts a bad idea.

I don’t want to exaggerate Warren’s crossover appeal. Today’s parties have such strong ideological brands that it’s difficult for any Democrat to attract much Republican support (or vice versa). What’s more, Warren is a social liberal. And if she ran, the GOP’s Club for Growth wing, which hates her with a passion, would spent vast sums demonizing her among its party base.

Still, the influx of working-class whites into the GOP in recent decades has created a wing of the Republican Party that is almost as hostile to financial elites as are many Democrats. For decades, the GOP has diverted these class resentments into cultural ones, but that’s become somewhat harder as generational change has made even culturally conservative younger whites less hostile to blacks and gays than their parents. It’s among these younger, blue collar, Republican-leaning whites where Warren could find her opening.

What makes Warren so politically potent is that she is heir to both the progressive and populist traditions. Like the early 20th-century progressive reformers, she’s wonky, high-minded, and wants to create new mechanisms of federal oversight. But like the populists who sometimes allied with those reformers and sometimes disdained them, Warren is openly contemptuous of insiders and elites—far more so than either Barack Obama or Hillary Clinton. And that’s the potential source of her-red state appeal.

The better analogy is not between Elizabeth Warren and Ted Cruz. It’s been Warren and Rand Paul. Warren’s crusade against Wall Street may appeal to young blue collar Republicans in the same way Paul’s crusade against the national-security state appeals to young liberal Democrats. Both Warren and Paul are exploiting a divide in the other party. Democratic elites are more hawkish on foreign policy than their party’s rank and file; Republicans elites are more pro-Wall Street than theirs.

If Ted Cruz wins the Republican presidential nomination, party divisions will calcify. If Elizabeth Warren wins the Democratic nomination, they may loosen. That’s one reason so many Democrats hope she’ll run.