Elizabeth Warren (D-Mass.) during her first hearing as a senator at the Senate Banking Committee on Capitol Hill in 2013. (Melina Mara/The Washington Post)

Democrat vs. Democrat! Intraparty fighting! Ohio's Democratic senator suggesting President Obama is sexist!

It might not be a "civil war" on the scale of what Republicans have experienced the past few years, but Senate Democrats' fight over a trade bill with Obama this week was one of the -- if not the -- left's most visible schisms in years. And it got personal.

In an interview with Yahoo on Monday, Obama said Sen. Elizabeth Warren (D-Mass.), who opposed him on the trade bill, was "dead wrong" and called her "a politician like everybody else." It was a burn from a former first-term, rising-star senator to a current one -- between a president and someone who set up his administration's consumer protection operation, no less. Translation: 'You're one out of 100. I'm the president.'

Also, he called her "Elizabeth."

Sen. Sherrod Brown (D-Ohio), who also opposed the trade bill, said Obama's comments about Warren were disrespectful and also noted that the president used her first name "when he might not have done that for a male senator, perhaps," according to Politico. The White House suggested Brown apologize for implying Obama was being sexist, while Brown spokeswoman Meghan Dubyak told the Web site that the "debate shouldn't be personal." Too late.

That this public Democratic fight comes at the beginning stages of Hilary Rodham Clinton's presidential campaign is significant. The last time the left was this split like this was last time she ran for president, when she and Obama tangled over the Iraq war in a lengthy primary. Since then, Democrats could have taken up fights against Obama on issues like the escalation of drone attacks, his lack of action on campaign finance reform, Guantanamo Bay, the Patriot Act and deportation figures that have eclipsed those during the George W. Bush administration. But the opposition never got as personal as it did this week.

Although Clinton doesn't face the kind of primary challenges in 2016 that she did in 2008, there are at least some dissatisfied progressive Democrats who would prefer a candidate like Warren, Bernie Sanders or Martin O'Malley. O'Malley, for his part, urged progressives in New York this week to unite behind him as the anti-Clinton, with Warren not running.

Clinton has made plenty of gestures toward progressives, and there is very little reason to believe the vast majority liberals are that unhappy with her, but it's hard to imagine a future-President Clinton not having some similar battles with members of her own party if she won the election. Obama certainly came from the liberal, grassroots wing of the party; Clinton does not.

During the Obama administration, Democrats have been largely quite unified -- and even moreso relative to Republicans, who've been split between tea party conservatives and moderate/establishment Republicans and have engaged in many very nasty, very public fights. But as this week has shown, there's a divide among Democrats too, and while it's not big, it's getting a little bigger.