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The bill was blocked by Senate filibuster in the current Congress.

An SEIU spokeswoman challenged the ads, calling them “smear campaigns,” and said their union won’t get into a back-and-forth over the affidavit and will remain focused on working on health care and jobs.

“We would invite AFSCME and Gerald McEntee” href=”/themes/?Theme=Gerald+McEntee” >Gerald McEntee to work with us to be part of the solutions here to help working families,” said Michelle Ringuette.

Mr. McEntee said unions themselves have not done a good job of educating voters about the Employee Free Choice Act and about unions’ importance to the middle class overall.

“It’s a story that bears better telling and we would be better off if we told it in a better, more explicit kind of way,” he said, adding that part of the problem is unions have been too eager for fights in the past rather than looking at the broader political picture.

“We could place ourselves as a union and as a labor movement in a position where all we do is throw grenades from the left. We’ve done that before,” he said. “Generally speaking, those grenades have blown up in our face, right? And you should learn after those kinds of things happen.”

Mr. McEntee said his union has told Mr. Obama’s team that it would like to see any stimulus spending bill include at least $100 billion in aid for state and local governments, split between the next two years.

His union endorsed Sen. Hillary Rodham Clinton in the Democratic primary race but worked hard for Mr. Obama once he secured the nomination, he said.

He detailed thousands of staff and volunteers, millions of phone calls and hundreds of thousands of door-to-door visits on Mr. Obama’s behalf, and said the efforts had an effect on some union members who were amenable to Mrs. Clinton but reluctant at first to support Mr. Obama because of his race.

“When you looked at numbers originally, they were bad numbers for Obama. They were bad numbers. But we were able to go out and talk to those kinds of people, educate those people,” he said.

He said his own membership is about 27 percent Republican. He said support for card check in his union runs in the “high 60s.”