"You're building them up, but in the process of building them up you're making them so unviable," Spicer said. "If you told me today that Hillary Clinton had announced that she isn't running [for president] and Elizabeth Warren is, I would be doing the biggest jig in my office."

But the senior Democratic aide simply pointed to the 2014 elections, when Warren traveled the country on behalf of Democratic candidates, drawing huge crowds. "Look at how many people show up when she goes and campaigns, even in red states," the aide said. "She has the pulse of what people are anxious about ... that there's a system that is working against growing wages and better-paying jobs. And that's exactly why people are crying out for. And that's why she resonates in Massachusetts, that's why she gets invited to places like West Virginia, Kentucky. She has a message for all audiences. It's a universal message."

Republicans plan to use that very message against Warren. Republican pollster David Winston notes that in 2008, exit polls showed that Americans felt that government should do more by an 8-point margin. In the wake of the 2014 midterm elections, that number flipped significantly; Americans now prefer that government do less by a 13-point margin.

"[Warren's] whole focus is government being the solution. What she's saying and what the public is saying are two different things," Winston said.

Democrats disagree. In a speech last month at the National Press Club, Schumer mounted a strong defense of a pro-government Democratic Party, pointing to Gallup polling that has shown that about a third of Americans prefer a more active government, a third prefer less government intervention, and a third want something in the middle. Those numbers have hardly changed since 2010. Warren, who will work under Schumer when she joins the leadership team, is a key part of spreading that message.

Warren's promotion to leadership only reinforces the idea that she speaks for the party as a whole, Winston and Spicer said. And as she gains influence within the conference, they say, it only helps Republicans. "I understand why Harry Reid and Democrats put her in leadership, but I wouldn't be surprised if a year or more from now they regret that," Spicer said.

But Warren's influence isn't limited to just the Senate. Pelosi forwarded a copy of Warren's entire floor speech on her objections to the Dodd-Frank provision in the omnibus to reporters Wednesday. And the grassroots effort lead by MoveOn.org, Ready for Warren, and other liberal groups to draft Warren to run for president is only raising her profile even higher.

Warren is hardly walking away from that position. She spoke at length on the Senate floor Wednesday, saying she would vote against the omnibus spending bill that will keep the government's doors open over the Dodd-Frank provision. She has worked tirelessly over the past few days to unite Democrats in the House and Senate around the issue, even holding a press conference with colleagues in the House urging Democrats in the lower chamber to pull their support from the bill until the Dodd-Frank language is removed.

And House Democrats did just that, forcing Republican leadership to pull the omnibus at the last minute and huddle with their members over how to pass the bill with just hours remaining before a scheduled government shutdown.

Warren wasn't alone in her opposition to the Dodd-Frank changes, but she was among the most vocal. For Republicans, that's good enough.

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