Over the weekend, the White House and Democratic Party  officials pushed back against criticism from Republicans that Mr. Obama and his political network were meddling in the Wisconsin dispute.

Administration officials said Sunday that the White House had done nothing to encourage the demonstrations in Wisconsin — nor was it doing so in Ohio, Florida and other states where new Republican governors are trying to make deep cuts to balance their budgets.

And, officials and union leaders said, reports of the involvement of the Democratic National Committee — specifically Organizing for America, the grass-roots network born of Mr. Obama’s 2008 campaign — were overblown to start with and were being inflated by Republicans sensing political advantage.

“This is a Wisconsin story, not a Washington one,” said Dan Pfeiffer, the White House communications director. “False claims of White House involvement are attempts to distract from the organic grass-roots opposition that is happening in Wisconsin.”