Washington (CNN) Elizabeth Warren's push to kill major trade negotiations -- backed up by the AFL-CIO's plans announced Wednesday to cut campaign contributions to its traditional Democrat allies to fight alongside her -- could become major headache for President Barack Obama.

Warren is spearheading a growing liberal push to undercut Obama's attempt to negotiate free trade deals with Pacific Rim countries and the European Union. Her beef: Corporations could gain the ability to challenge countries' laws under a complicated provision that's routinely tucked into new deals.

The innocuous-sounding "investor-state dispute settlement mechanism," critics on both the left and the populist right fear, would be like an independent, international court, with the power to force the U.S. government and American corporations to abide by its rulings.

The issue pits Warren against her own party's president, and on the same side as populist conservatives. The Massachusetts Democrat took aim at that provision on a conference call hosted by liberal groups on Wednesday, saying it should "raise alarm bells for everyone."

"The name may sound a little wonky, but this is a powerful provision that would fundamentally tilt the playing field further in favor of multinational corporations," Warren said. "Worse yet, it would undermine U.S. sovereignty."

Lending muscle to Warren's opposition is the AFL-CIO, which announced Wednesday that it is freezing contributions to Democratic candidates in order to pump its money into the battle to defeat Obama on trade -- a clear implication that union money will only be flowing to lawmakers who work against their party's president on the issue.

Photos: Hillary Clinton's potential challengers Hillary Clinton's potential challengers – Sen. Elizabeth Warren of Massachusetts has repeatedly said she's not running for president, but the Democrat -- a favorite among progressives -- has been urged to run by populists in her party. A first-term senator elected in 2012, Warren is known for her attempts to take on Wall Street -- both as a senator and as the creator of the Consumer Financial Protection Bureau during President Obama's first term. Hide Caption 1 of 5 Photos: Hillary Clinton's potential challengers Hillary Clinton's potential challengers – Maryland Gov. Martin O'Malley has been laying the groundwork for a potential presidential campaign, headlining 80 fundraisers and 40 campaign events around the country. A two-term governor, his time in office ends in January. The Democrat's resume as governor includes legalizing same-sex marriage, repealing the death penalty and enacting strict gun-control laws. Hide Caption 2 of 5 Photos: Hillary Clinton's potential challengers Hillary Clinton's potential challengers – Vice President Joe Biden and Hillary Clinton faced off in the early 2008 Democratic primaries, and both are weighing 2016 bids. A 2016 run would mark Biden's third bid for president; he also ran in 1988. Before becoming vice president, Biden served as a U.S. senator from Delaware for 36 years. He has already made visits to early primary states this cycle on official White House business. And if Clinton runs, Biden said her decision wouldn't affect his own. Hide Caption 3 of 5 Photos: Hillary Clinton's potential challengers Hillary Clinton's potential challengers – U.S. Sen. Bernie Sanders, an independent from Vermont who caucuses with Democrats, has been testing the waters for a 2016 bid. He's hoping to push an agenda that focuses on income inequality, climate change and campaign finance reform. Sanders has already traveled to early primary states such as Iowa and New Hampshire. Hide Caption 4 of 5 Photos: Hillary Clinton's potential challengers Hillary Clinton's potential challengers – Former Virginia Sen. Jim Webb has said he's "seriously looking" into a 2016 bid for the Democratic nomination. Webb left the U.S. Senate at the end of his first term in January 2013. He's a veteran of the Vietnam War who also served as Navy secretary and assistant defense secretary. Hide Caption 5 of 5

As soon as Warren's conference call started on Wednesday, the Obama White House was pushing back. U.S. Trade Representative Michael Froman's office sent out an memo intended to show that the provisions Warren was critiquing wouldn't change anything in terms of domestic laws -- and would actually increase U.S. businesses' protection abroad.

Warren's emergence as a leading critic of U.S. trade efforts could derail Obama's attempt to add the 12-country Trans-Pacific Partnership to his legacy.

But the liberal opposition to the deal -- which liberals have dubbed "NAFTA on steroids" -- could pose a big challenge to Clinton's nascent 2016 presidential campaign as she tries to stave off a primary challenge from the left.

Clinton embraced the Pacific Rim negotiations during her tenure as Obama's secretary of state, as she led the ballyhooed pivot to Asia -- with the trade deal as its economic underpinning. Though her spokesman didn't respond to questions about her stance on the deal Wednesday, Clinton said the deal could be a boost to U.S. workers and businesses in her memoir last year.

"It's safe to say that the TPP won't be perfect. No deal negotiated among a dozen countries ever will be -- but its higher standards, if implemented and enforced, should benefit American businesses and workers," she wrote.

Warren, though, is leading a populist charge against the deal. But she called on "conservatives who believe in American sovereignty" and libertarians to back her position, too.

Many of them are already there -- for different reasons. More than two dozen Republican lawmakers, as well as right-wing and tea party organizations backing their positions, deeply distrust Obama and are loathe to hand him any additional power.

And to get the Pacific Rim deal done, that's exactly what they'd have to do.

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Trade policies like the "investor-state dispute settlement mechanism" that Warren was lambasting are as complex as it gets -- with the nitty-gritty details unlikely to captivate most lawmakers, let alone voters.

But the broad strokes make for obvious politics. Obama, for example, is requesting "trade promotion authority" -- a power every president since Nixon has had. It would allow him to submit trade deals to Congress for guaranteed votes on a limited timeline, and with no amendments. In a rare show of unity with the White House, Republican congressional leaders favor the measure, acknowledging it's the only way to get other countries to make the concessions necessary to finish negotiations and lock deals in. But populists on both sides say it's a the kind of give-away that Obama hasn't earned.

The battle over trade promotion authority, though, would only be the opening salvo in one that could come late in Obama's presidency or early in his successor's first term over the Trans-Pacific Partnership.

Lawmakers who have clamored for ways to pressure Asia-Pacific countries to stop manipulating their currency or to import more American-made automobiles are all but certain not to get what they want. Liberals will question whether Obama got the best deals possible on labor and the environment. Conservatives will demand more protection for businesses' intellectual property -- and less ability for foreign companies or countries to challenge U.S. rules.

Warren is among the highest-profile critics to emerge in the Senate, though a handful of House Democrats (often led by Rep. Rosa DeLauro of Connecticut) have been hammering away at the Trans-Pacific Partnership for years.

Warren sought to bring a quick start to the looming trade debate on Wednesday, saying it's time for U.S. trade negotiators -- if they're sure they've got a strong deal in the works -- to show their progress.

"If they are sure they have fixed this problem, they need to show all the new provisions," she said.