“On every front of the battle to take back the House — fund-raising, volunteers, candidates — what is happening in Madison is helping,” said Representative Steve Israel of New York, the chairman of the Democratic Congressional Campaign Committee. “People who we have talked about running now seem more energized by what’s happening. They understand that this is part of an ongoing Republican attack on working families, and they want to fight back.”

Republicans counter that the energy will not last.

Scott Fitzgerald, the Republican majority leader in Wisconsin’s Senate, said that by 2012, the fallout from this bill seemed more likely to him to harm Democrats’ hopes for the state (which Mr. Obama easily won in 2008). “I think once some of the union members wake up and say, ‘I’ve got to wake up and write a check to the union every month?’ union membership may quickly drop, and some of their power falls apart,” Mr. Fitzgerald said.