WASHINGTON — Hillary Clinton just kicked off her presidential bid on Sunday, but progressives have already begun a campaign of their own to shape the financial policy debate ahead of the 2016 elections.

Sen. Elizabeth Warren, D-Mass., delivered a wide-ranging address on Wednesday, laying out an agenda for tending to "unfinished business" in the financial industry in the wake of the financial crisis and the Dodd-Frank Act.

The Massachusetts Democrat has repeatedly put to rest rumors that she plans to run for higher office, but her proposals appeared designed to influence the positions that Clinton and other presidential contenders take.

"Warren wants to ensure that big banks are part of the 2016 presidential election. This is a clear notice to Hillary Clinton that she's going to have to be tough on the banks to avoid a war with Sen. Warren," said Jaret Seiberg, a policy analyst at Guggenheim Securities.

Warren, who has become a key spokesperson for the progressive wing of the Democratic Party, detailed a number of specific policy proposals designed to break up the big banks, punish bad financial actors and increase oversight on auto dealers and the so-called "shadow banking" system. She pushed for tougher rules to keep banks in line, but also lambasted regulators for not doing enough on their own.

It's not yet clear whether the Massachusetts senator is putting pen to paper on many of these proposals, many of which would require legislation, but they are unlikely to gain traction in the short-term while Congress is under complete GOP control. Republicans remain deeply skeptical of Dodd-Frank, and much of what Warren is pushing for amounts to going further than the 2010 financial reform law.

But Warren's ideas are likely to play into the presidential debate, particularly for Clinton, who has traditionally been seen as more pro-Wall Street.

"You've already seen" an impact, said Seiberg. "Hillary Clinton is taking a more populist tone in the early stages of her campaign than she exhibited during her tenure as senator. Speeches like this from Elizabeth Warren force Clinton to the left."

Marcus Stanley, policy director at Americans for Financial Reform, said Warren's speech lays "down the gauntlet for people in terms of taking specific, strong steps — including steps that go beyond Dodd-Frank — to reform Wall Street."

"That's very meaningful in terms of the challenge it puts to people to say whether they're in favor of that or not," he said.

Former Maryland Gov. Martin O'Malley, one of the few other policymakers thought to be vying for the Democratic presidential nomination, has already staked out positions closer to Warren's view.

In an op-ed published last month in the Des Moines Register, O'Malley agreed that Dodd-Frank "did not go far enough."

"The largest banks should be broken up into more manageable institutions," he wrote.

Like Warren, O'Malley also called for harsher penalties against banks for wrongdoing and a reinstatement of the Glass-Steagall Act ban on mixing commercial and investment banking. (The ban was repealed by the Gramm-Leach-Bliley Act of 1999, which was actively supported and signed into law by President Clinton.)

Hillary Clinton, previously a New York senator, still retains strong ties with the financial industry.

It's possible she will have to naturally pivot to the left of her husband, who was also considered a centrist and friendly to Wall Street, but that may not be enough for a frustrated and increasingly vocal progressive crowd led by Warren and others.

"Hillary Clinton will probably be better served by running as an Obama Democrat — more liberal — than a Bill Clinton Democrat, because in order to win she is going to need to juice Democratic turnout," said Kyle Kondik, a political analyst with the University of Virginia's Center for Politics. "That said, I think there are many on the left, including Warren, who do not fully trust Clinton. Once the primary is over, they have no influence over her. So it makes sense that forces on the left will be trying to lean on her now to push her towards their positions."

At the same time, Warren's approach on Wednesday was notable for its focus on the role regulations play in a creating a better functioning marketplace — an oft-cited goal for many Republicans. She framed her concerns around the need for clearer and simpler regulations, which in turn support business. That notion, she said, should transcend traditional party lines.

"For too long, the opponents of financial reform have cast this debate as an argument between the pro-regulation camp and the pro-market camp, generally putting Democrats in the first camp and Republicans in the second," she said. "But that so-called choice gets it wrong. Rules are not the enemy of markets. Rules are a necessary ingredient for healthy markets, for markets that create competition and innovation. And rolling back the rules or firing the cops can be profoundly anti-market."

It's possible that focus could help her ideas win support on both sides of the aisle

"I have not seen her so clearly place everything in this pro-market context, and that, I think, is very much reaching across the aisle," said Simon Johnson, a professor at MIT.

Warren's tone could resonate with populist conservatives who share her skepticism for big banks as well as big government.

"Warren is pushing Clinton not just to the left but to a more populist tone," said Seiberg. "The far left and the far right hate the big banks equally. So Clinton's rhetoric on the big banks may be similar to what you hear out of Rand Paul or Marco Rubio or others on the GOP side."

— Rob Blackwell contributed to this article.

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