DETROIT — The United Automobile Workers union, a primary beneficiary of President Obama’s decision to rescue domestic carmakers, is now trying to return the favor” Bob King, president of the U.A.W., spoke Friday outside Ford Field in Detroit.
     As Mitt Romney prepared to deliver an economic address here on Friday declaring Mr. Obama’s three years in office a “failed presidency,” hundreds of union members gathered on the top level of a parking deck as a freezing drizzle fell.
     “Thank you, President Obama!” shouted the union’s president, Bob King. He gripped a bullhorn as he exhorted the crowd, “Everyone!” They roared back, “Thank you, President Obama!”
     It was the beginning of an effort by the U.A.W. and others in the labor movement to put their vast political organizations into motion behind Mr. Obama, testing their power in a difficult economy after years of declining membership. This is an election that both parties say could turn on their ability to win over working-class voters in the industrial Midwest, where battlegrounds like Michigan, Ohio and Wisconsin could determine the outcome.
     Mr. Obama will meet in Washington next week with 1,700 U.A.W. leaders to talk about steps to ensure that the economic recovery lasts and to signal to them that he shares their concerns about income inequality and preserving the middle class, the White House said on Friday.
     One of organized labor’s motivating issues in the election is addressing disparities in wealth, a topic that Mr. Romney, whose worth is estimated at as much as $250 million, inadvertently drew more attention to Friday when he said in his speech that he and his wife owned four American cars, including two Cadillacs. And Mr. Romney has criticized the auto bailout as “crony capitalism” that benefited “union bosses” at the expense of taxpayers, a position that has left him battling to win working-class voters in the face of union opposition.
     In an attempt to outnumber Republicans at the polls in November, union officials are getting an early start with voter registration drives in their plants. Successful efforts to curb collective bargaining rights in neighboring states like Wisconsin and Indiana are adding to a sense of urgency already heightened by the steep decline in ranks. The union has about 400,000 members — less than a third of its size 30 years ago.
     Mr. King has told local chapter officials they should aim to have conversations with every member they oversee about the importance of voting in this election. Other officials are busy raising money for the U.A.W.’s political fund.
     And a new online organizing network for the union, called Gimme Five, is constantly adding new members, who are notified by text message and e-mail about events like Friday’s protest, a joint effort planned with a local Democratic Party group.
     “We plan to be very active in this election,” Mr. King said in an interview. “We’re building a broad coalition that we hope will help President Obama get re-elected.”
     The U.A.W.’s efforts come on the heels of activities by other large unions that have rallied to the president’s side, like the American Federation of State, County and Municipal Employees. Last month it spent $1 million on advertising attacking Mr. Romney in Florida. Now it is preparing another round of advertising in Ohio, which will hold its primary on March 6.
     The “super PAC” supporting Mr. Obama joined forces with the Service Employees International Union to run commercials mocking Mr. Romney for saying that he pays an income tax rate of only about 14 percent.
     While the federal loan package to General Motors and Chrysler, which cost about $80 billion, is hailed by the U.A.W. and other unions as a success, Mr. Romney and many other Republicans see it as an example of government meddling at its worst.
     In the industry restructuring that followed the auto rescue of 2009, the U.A.W., long a major contributor to Democrats, was given an ownership stake in Chrysler and became one of G.M.’s largest shareholders. Pensions of some union members and retirees were left intact, while salaried, nonunion employees took big hits.
     The fight over the role of organized labor in American business is likely to be one of the more divisive of the election, with Republicans arguing that unions harm competitiveness in a global economy and Democrats saying that they are necessary to preserve a middle-class way of life.
     That debate is already playing out in Michigan. In an appearance before a supportive Tea Party crowd north of Detroit on Thursday night, Mr. Romney committed himself to rolling back the rights of unions in a state-by-state effort to end mandatory enrollment at companies where a union has formed. “It is extraordinary that we force people to join a union whether they want to do it or not,” said Mr. Romney, who was born and raised in Michigan and is the son of a former governor and auto executive.
     In Michigan, which is slowly adding jobs after losing more of them in the last decade than anywhere else, it may be harder for Republicans to argue that unions are a drag on business.
     The assembly lines here are rolling out more cars. Parts makers are setting up booths at job fairs in search of new engineers. And factory workers at General Motors will soon receive $7,000 bonuses.
     Unemployment is still high. But at 9.3 percent, a percentage point higher than the national average, it is nearly two percentage points lower than it was last summer.
     Eric Watters, 41, a chief steward at the Chrysler assembly plant in Sterling Heights, said it still distressed him to think about the day in 2009 when his supervisor announced that the factory was shutting down. They were told to cover all the equipment as if they were never coming back. “It was an eerie feeling,” Mr. Watters said. “Your entire life is hanging at the very end of the string.”
     But about three years later, the plant has added a shift and is bringing in new workers — workers whom Mr. Watters and his colleagues are now trying to register to vote.
     “Being a union man, you have to be politically active,
because our strength is in numbers,” he said.
     At the rally on Friday, many U.A.W. members said that the near-death experience of American carmakers had energized them in a way they did not expect.
     “We’ve been threatened with losing our jobs,” said Percy Johnson, a tradesman who works at the General Motors factory that produces the Chevy Volt. “That’s what this is about. And we’re motivated like never before.”
From the New York Times Online