It is not at all clear whether the leaders of the amorphous movement actually want the support of the Democratic establishment, given that some of the protesters’ complaints are directed at the Obama administration. Among their grievances, the protesters say they want to see steps taken to ensure that the rich pay a fairer share of their income in taxes, that banks are held accountable for reckless practices and that more attention is paid to finding jobs for the unemployed.

The movement has chosen not to have a spokesman and did not offer official comment on the Democrats’ attentions. But whether sought or not, the blessing of senior Democrats holds the potential to give the movement added heft in the same way that the role of senior Republicans like the former House leader Dick Armey did for the Tea Party as it grew from an offshoot movement to a much more organized and potent force.

The protests also provide yet another bright dividing line between Democrats and Republicans in Washington — one that seems likely to help shape the competing themes of the 2012 presidential election.

Democrats and Republicans were already largely divided over the Dodd-Frank legislation, which set out hundreds of new restrictions governing the way financial institutions operate and are regulated. But while the regulations were dense and difficult for many Americans to understand, much less seen as a rallying point, the widespread images of the sprawling protests have offered both parties a colorful and powerful symbol around which to frame their perspectives.

Leading Republicans have grown increasingly critical of the protests. Eric Cantor, the House majority leader, called the protesters “a growing mob,” and Herman Cain, a Republican presidential candidate, said the protests are the work of “jealous” anti-capitalists.

The Republican National Committee is also eager to use the protests against Mr. Obama.

“The protests began with anger aimed at Wall Street, but the anger is also directed at the failure of leadership in Washington and that starts with the president,” Kristen Kukowski, a spokeswoman for the committee, said Monday.

The protesters “realize that if they want change, the one person most responsible for the status quo and for making change is President Obama,” she said.