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Those unions backed Ms. Falk, a former Dane County executive, who promised to veto any budget that didn’t restore collective bargaining rights. Mr.  Barrett, who has clashed with unions during his tenure as mayor of the state’s largest city, pledged only to try to restore those rights.

Despite that rift, both Ms. Falk and major union leaders issued statements supporting Mr. Barrett and promising to work together to defeat Mr. Walker.

Mr. Barrett may have the unions, but Mr. Walker has the money. He has tapped his status as a national conservative rock star to raise $25 million so far, most of it from out of state, shattering fundraising records he set during the 2010 race.

Mr. Walker had $4.9 million in the bank as of April 23, compared with Mr. Barrett’s $475,500. Mr. Barrett has raised $831,500 this year so far.

Mr. Barrett, 58, has been popular in Milwaukee, where he won re-election in April with 70 percent of the vote. He previously served eight years in the state Legislature and 10 years in Congress.

Associated Press writers Marilynn Marchione and Carrie Antlfinger in Milwaukee and Todd Richmond in Sun Prairie, Wis., contributed to this report.