According to a New York Times article, After Push for Obama, Unions Seek New Rules, one big goal unions want to accomplish, with President Obama’s help, is passage of legislation that will make it easier for workers to unionize.

The NYT says,  “Labor’s No. 1 priority is a piece of legislation called the Employee Free Choice Act, also known as the card-check bill. The bill would give workers the right to join a union as soon as a majority of employees at a workplace signed cards saying they wanted one.”  Excerpts from the article:

• With union membership sliding to 7.5 percent of the private-sector work force, one-third the rate in 1983, unions see enactment of the bill as the single most important step toward reversing their loss of membership and power. Some labor leaders predict that if the bill is passed, unions, which have 16 million members nationwide, would add at least five million workers to their rolls over the next few years.
• Mr. Sweeney said that in the last four days of the campaign, 250,000 volunteers from A.F.L.-C.I.O. unions made 5.5 million phone calls and visited 3.9 million union households. All told, he said, unions reached out to more than 13 million voters in 24 states, with some undecided union members being contacted more than 30 times through phone calls, household visits and workplace conversations.
• Union leaders say they were pivotal in helping Mr. Obama win several battleground states, including Florida, Indiana, Nevada, Ohio, Pennsylvania and Wisconsin. According to a voter poll by Peter D. Hart Research Associates, 67 percent of members of A.F.L.-C.I.O. unions voted for Mr. Obama, a Democrat, and 30 percent for his Republican rival, Senator John McCain.
• While the Chamber of Commerce seems ready to cooperate with organized labor to back an economic stimulus package, Mr. Donohue, the chamber’s president, said it would be unwise for Mr. Obama to embrace the Employee Free Choice Act when the economy was in such bad shape. He said the bill — along with other labor-backed bills that would raise business costs, including one that would guarantee most workers seven paid sick days a year — would hurt companies when many were struggling.
• Chamber officials voiced confidence that they have the backing in the Senate to block the bill, a move that might cause business and labor to negotiate a version with compromises. Among the compromises floated would be keeping the secret ballot vote, but holding the vote just a few days after the union requests an election. Other ideas are to give union organizers access to workplace sites and to limit employers’ ability to campaign against the union.